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New Revolutions in Particle Physics: Basic Concepts  Lecture 9
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plant Stecher University a very
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important concept of particle physics of the field equations of course the equations of motion on the field describing the particles we describe HMOs onfield firmly on fields busy electromagnetic field for reason satisfying quite the form of the equations as well as wave equations involves derivatives of a field with respect through space with respect for kind and the fuel itself embossed rivers a field field itself are Ruiz a few undifferentiated Crowley code these equations we just write down all of the equations for all of the fields he Ali could do that the right down the equation of motion for electromagnetic field America electron field for the fields the system and that would just be the equations of motion but in our own standards classical mechanical systems field theory even quantum field theory the equation of motion fully calm from Lagrange year over grungy as a very important concept of classical mechanics choir mechanics and quantum field theory or gradually as an object you do certain things to generate all of the equations of motion of the system not just 1 by 1 the equations of motion for each field about it contains in 1 simple expression want condensed compact expression all of the equations of motion system of fuel sources of degrees of freedom and in general EU grungy an idea in classical mechanics very closely related the principle we stature and when into a year I'm going to just very quickly remind you of the connections were Worldwide unit is what depends on our how you generate the equation of motion and do 1 of 2 examples that that's all classical physics and then explained to you what the meaning of the Lagrange In quantum mechanics same grungy and accept expressed not from the classical field of quantum field has a totally new meaning in terms of quantum mechanics are dictates the motion of particles the interaction between particles cross sections for collisions all sorts of things it codifies Varese aboard Russia 1 compact our idea OK were Burundi another system of fields the court script L is a function horror L of for the simplicity with just the imagine 1 field work for you would you do if you have more field posing as 1 field fiery Granzien on the field and gave it depends on the derivatives of a field with respect for prime and space so it could depend on the river field at the and derivatives of the field with respect exwife Missouri for more compactly depends on the field and the derivatives field With respect X new derivative with respect to x 5 now will go to a grungy degenerative Furyk wages are not going the April this work for through argue for these equations we've done that passed several part tell you what the rules are rules are generally the equations of motion you differentiate Boulevard With respect to the derivatives of a field for example Nunavut on L. with respect to tool derivative of 5 with respect to show you examples looks abstract from our rent the you differentiate with respect to you your bath the derivative with respect X of the derivative of our ground Jim with respect to the gradient of field along the xaxis thinking thing for white Missouri and then you said that equal the river around with respect to field the South France depends on the field of itself that is the equation of motion for a field 5 your Grudzien depends on several field renewed the same thing over Norfolk each 1 of the few and that generates the system of equations are 1st firstever below an example as we go on whom do some examples but let's just do the very simple example the see Abbas works as a symbol of scalar field of very simple scalar field show Bush Field puzzle run GM which is equal to squalor and the river or fire with respect the kind squared with conventional 1
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half the river fire with respect the Times Square minus the same half a river of fire with respect to x square same thing of wine and zebra all right our both that's a minus sign here minus sign finally minus functional course of 5 or you beautify that's the nature of the Lagrangian of a simple scalar field but always no more or less see if we can work out what the field equations are your 1st begin by differentiating will run runs in with respect to call fight . he just got 5 . 3 5 and let us simplify the that were convinced the notation instead of the 5 defined by the X tried Viney X 5 X means the removal firewood which act likewise for wines yellow you ever will be in here that will be in here right OK Salesforce differentiator Lagrangian with respect the fight not yes like that right here fight at square 1 half RGa square whoever derivative with respect back is justified barber shop
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differentiate 1 half by buybacks cornered with respect the viaduct self differentiating through cancels a onehalf you just get quite back but then you have differentiate again with respect time that makes a fight bubble wrap derivatives 2nd Prime derivative now the space derivative terms come with the office of starting from the perimeters or explain why in a moment but just accept that they come in with the office of starting to get exactly the same kinds finger with the opposite signed with 2nd based 2nd derivative of fire with respect to x squared the same thing with wine theme and then on the right hand side we have a derivative Lagrangian with respect the fine the only place where phi itself for cars on differentiated is in view of our sold or gamma righthand side minus derivative of view with respect for 5 that's that's a former field equations for very very simple scalar field are some examples of via farright the simplest example of your fire would be a constant but that it would have no derivative with respect of firewood leaving contribute here interested in or are we could have something leader in the FRA that's all right to grab some removing your party but if if this incidentally is field energy real fight field with me is unbounded from below means in order to be used as a linear function of far that means energy the minimum of the energy instead we fall off negative that best I could be 1st interesting example it is the 1st Vice square feet of fog physical something proportional defy square fire a proportionality constant but called constant and squared but put to it is no content America and quit or 2 is just some I call square or through because it has some physical meaning that will feel more however have if I differentiate and squared over fire squared with respect the FIA that gives me and squared 5 differentiating your fire with fire would just give me and square 5 light so a again so boy of equations Phi double by minus revivify with respect to x squared 5 is he Kwong for minus I think and squared that is a very very basic form for a wave equation both in classical field theory quantum field theory are electrodynamics also situation is wave equation shows what does it say bomb the relationship between the energy and momentum of quantum of the field far more 1 acquire mechanics quantum field theory energy is related the frequency differentiating twice always gives us a factor of minus tool start minus Omega square we have a way of we have a wave function which is performed he each have Omega see perhaps times each of a minus are you OK X on a flight
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differentiate with respect property that brings them a factor of our Masada if I do it twice it gives me on my Omega square times 5 find what happens if I differentiate with respect the export Rico factors of Katie Hoff case selects from your boss Kerry x squared farright case why square case of disease squared off crimes I have
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started we have reminders squared
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readers crossed off a fiveyear plans for an hour north this wave equation tells us is just a relationship between all may case square how's or start Omega squared minus case squared with you and square that's really the whole content of a wave equation for way of moving down our particular axis tells us a bomb maker squared equal buddy at Omega square physical decay squared questioned square if we remember what's work in our favor you with stage Oracle's 1 far bar Accorsi ones the Albany Ga it was nothing but the energy or maybe is related to energy by a factor of each energy square he calls momentum squared cause and squares this is the usual relation if I want to make it that I worked with the speed of light Back in there would put poets advocacy squared over here and seek support here when you question for the units in which a speed of light 1 misaddress E equals a square Eagles square square was the usual relationship between energy and momentum if we interpret and as the merits of a single quantum could show what this equation tells us then is really nothing but the relationship between energy mass and momentum with the stipulation of parameter him here the massive apart so that's quite show in fact will appoint them right kg yr it's important you want your equations in and to be relativistically invariant variant the Lorentz transformations the only thing you have to do to keep them invariant under Lorentz transformations is make sure the program you scalar is really a scalar and transforms gala Lorentz transformation your equations of motion will be invariant Goran that's why minus sign here member wherever I want every doing special relativity might starring our relationship between space and time OK so that's the basic set up program gyms a river quite simple there could be several field around here and they could be interacting with each other and from where another hour we give you another example of just 1 field supposedly fighting proportional defy squared would also put something else for example who are GE times strike you I bet it would be another chairman he orders would be another tournament here which were biggest miners Regine fi square the equation emotional would no longer be linear really means only contains 1st powers of derivatives and field solve of the equations linear amid you could hear solutions in your new solution but now we have a nominee of equation more means quadratic party quadratic cubic any kind of higher power fight so we see a pattern of is things and all grungy whichever quadratic and Eva derivatives on the field itself leave told me any recourse Asians and things which are higher powers quadratic lead and nonlinear equations Marlene equations means solutions on 1st puts take the case of linear equations array of linear equations and support we have some from wave moving down and it's a social and now we have another wave superimposed about superimposed yet another wave packet From the same field moving every left instead of right and they pass each other well just equations emotional leader they will just go right through which when you're equation of school right through each other R and the a solution will be means just after work for this is solution but this is emotion and some of the solutions just nothing but to wave packets coming at each other for all kinds of social would just remains the sons of the original solutions and all will happen was the past right to each other com among the other and without scattering without performing are during the time that pasta which over there may be some interference but then the press to each other and to wave packets will lower seperate on the form on the other hand if there are nonlinearities Mcquage motion that means the wave packet scatter the influence each other and might not only scattered might break up might do all kinds of things much more complicated endeavor that create scattering in particular scattering of waves which often ran elections whatever OK so that's what nonlinearities higher powers to hear causes the wave packets be nonlinear and scattered another example just to show you what you could condone it is you might have to feel for simplicity to scalar field make scalar fields we would take these terms here has a right Porto feels fine render union aware nor a Greek letter yes rout of viral so another possibility for around here not is nothing special about the use of this writing down reign our 1 half being 580 squared assessing thing I've written here just short of up and made simple stands fight not squared minus drew fire with respect square and so forth just heard the short hair and do the same thing for McCaw overall theme you role squared and then we can ever something which some of these some potential energy which depends on both fine emerald service could some fine Ross example it could be and Vice squared or tool from other constant got caught capital and Square Raul square or to the best of all whitehaired supposing that was all I had been in the field equations would be couple separate field equations for flight role doing this operation on Friday we would get last fight double minus 2nd river fire with respect to x where bad food is equal rules and squared mines and squared find we get the same crime suffering from rural road of about minus 2nd row by DX squared up 5 equals minors big and squaring role
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another war as we would just get Cone separate independent wave equations with tone different parameters square began M Square and the 2 parameters we correspond with masses Of the distinct fields what quanta masses of a quarter of the 2 distinct fear this will be a system of talk kinds of particles fight roh quarrel with 2 different masses and began now I could have something more complicated we could add for example lets a had rolled ponds 5 square begin picked at random nothing special about Chris when work out the equation of motion for 5 we have on the righthand side of the river of me with respect the fight was a derivative of TV with respect for fighting while as just a approved my River overview of respect fog is just twice ruled fight differentiating squared could request far off on the other hand the equation motion for role we have the former righthand side minus remove movie with respect the role just equal to minus 5 square OK so here we see an example of an interaction between 2 fields terminal Grand which involves both field terminal around Jim involves both fields some nontrivial way the result will be the a wave equation for 5 will contain role and the wave equation role contain far if television this is not quadratic the equations of nonlinear nonlinear and Koppel that means that a wave packet of fire you will scatter a wave packet of Raul a wave packet of roles Gavra with packet of far from together and road do things not just Esther whichever 0 but his pastor rich over still somehow be terms and Lagrangian white role fiery square on telling us something about interaction between the quiet telling us the quanta of the fuel scatter each other as workfare workers indicating Rios shows here How else about energy and momentum Mr. tells about mass of we didn't have we didn't have this nonlinear terms the content of this equation would just be squared the Omega square articles K. square for some square at stories in this journey tells us about the interaction between quarks as classical physics such classical field theory Nutshell colony write down another example for your mother example is the Dirac equation consumer Dirac equation was Dirac equations it has the form Va a priori eyes go on but sigh . it is equal to half a derivative of vector X our society because of high here also everybody remember class and and beta size they was a matrix thought was a collection of 3 matrices really means our for 1 Beebe IDX warned off a coup d but X 2 4 of Dirac equations can it be written terms or grant yes it can be written in terms of Lagrangian will grant is just our I sight BAGHDAD river sigh with respect complex Carduus side our plants figures plus the other important strike Baghdad I'll the rim of fire with respect to X M and fiery plus side BAGHDAD Beta Phi times and sometimes you this is go around here this laboratory if you do the same on operations will give you a Dirac equation vessel grudges for Dirac equations when the ruins found
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portend for us right now now is for indicate that there is a low grungy and which generates the Dirac equation the same way that the scalar field equation was generated from Lagrangian scalar field that's got Dirac matrices in it what's more complicated it's a multicomponent field but nevertheless that were Dirac field is generated or Dirac wave equation it is generated From for granted could this with just give you the ordinary Dirac equation now supposing it was another field anger problem possibly a scalar field of scalar field of bows I feel how might you within alien also Granzien the Taylor field another where Our skill fewer grounds you review just PM square a baby who do like you a step that closer is to a place all a baby is important not known for what are we important thing is that we can't Koppel Dirac field for scalar field which essentially means make the scatter scalar field scattered Dirac field direct fuel scout scalar field but pulling turns on what Grandview which cobbling together for example something like a dagger now trying something away more sigh daggers curbside nor but there is not warranted side Prince archives fog this is not really quite legitimate because about Iran's variant if you wanted to make it warrants in an unmarked car export Mr. commodity fond of the back of some of the rack matrix ology but you adjust planned a base here that would make it look the baby is just a matrix doesn't change structurally appreciable worry that if far from 2 sides from party and that would give you an interesting field theory where 5 fields scabicide and sigh fields ratified the whole thing big black Pemex Vice commands size they scattered Charlie With yachts Sasabe but not a that society and same Bader I'm tried so it's almost as and was being replaced by a scalar field here this is the way ball every drop this foreground you would generate false the equations of motion for signing and for far off it would be a Dirac equation with an extra term proportional defined and the arm of scalar field equation with extra terms that would have sigh about in solo this is the pattern this is the way quantum field theories are expressed their codified by writing down 0 Lagrange here grungy and things were chair overture very simple way he expresses all of the content broad dynamic all the interactions between these fields I don't that's classical field theory classic or wave packets scattering of a classic where packet water now quantum field theory prepare you very briefly what what this has to do with interaction between particles will rails it pours badly about the scattering of particles and how would represent for example are products of field field on the half hour of creation and annihilation operators Soviet tank of fuel for example and I wrote stick a simple example fight Q. What does that represent when you think about it from the the creation of a moderation fine book contain both creation operators call a pluses quotes 18 Martinez who is very schematic nor detail contained various creation and annihilation operators who was killed they will contain all kinds of terms curtains which can absorbed are entirely free particles CAD being minus Q turned terms which could create 3 particles terms which can eat to particles spread out of 3rd and so so forth so YQO has a meaning in terms of particles coming you and particles going out particle convened to particles go out Apr . X that's what
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fight Cuba vexed represents from of quantum mechanical point of view IQ directs represents 1 particle coming in and splitting into 2 would at the point Poindexter but there are many terms In setting up fog Q. directs the various terms correspond to possible things which look like Paris mainly to particles communion 1 particle going out there's a possibility of free particles born out just produced at the origin 3 particles coming in a while so I missed anything they want particle those 2 particles total 1 no particles got 3 3 particles disappear but the kind of thing which will be codified by FIQ but the fact run June represent New Year's some of the terms represented actions like this we all the terms quadratic behind powers to represented directions like this the quadratic terms Robert quartered here these represent just the motion of a particle on the emotion of the undisturbed particle so as to have at work we are at stake West Egg there are a lot of time for derivative of fine with respect to x square lonely figure of the forlorn way for the removal of society is a group of fine and 1 pouring minus foggy and neighboring Corning what's cortex prime that's what contributors right derivative is basically a yarn about a different feel it to neighboring points and again schematic 40 shall square as for flight the fiery respect X spans for masseuse for born have for the 1 hair Fiore but if I miss 1 half 5 of X squared or have far ER next prime square of important pouring terms which is we are trying our X Pyrex price Mr. tons of ivory and
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arresting where they do duel the absorber particle appointed produce another particle exactly the same point they might need to particles of the same point or memory take buddy comedy particle point DEC's absorb it and they just spit it back out the same point so they don't move particle around they just uh restore past Morris this 10 he absorbs a particle at time and should appoint X or vise versa another lawyers what it does is it moved article from . Poindexter trying to absorb it fines Alexei price and emitted point for effect thought of that very few if any of this point extra support that Prime just moved the article from that's the nature of these quadratic terms will to remove particles 1 . 1 if you want to imagine emotional particles from 1 . 2 with distant point you might so we multiplied terms of grants you together many arrange Barth so that the 1st time would move the particle from next Brian next viral expired bubble Prime prime vegetable climb forth bike simply the quadratic terms Amir ground you governed the motion of the undisturbed article us with our Mayor connected with free motion over particles prefer prefer probe on the other hand the nonlinear terms not only in terms removed terms which are cubic for example where you grab hired Jacoby quartic they take particles and bring them together and scattered them or annihilate them create new particles so that's what program Jim browsers asserted codifies these interactions reserve his promises to use in a very very condensed way how how how yes a Kyoto so review following call difference between this and next prime was just quiet dissidents L Arab states so right do after under Merkel factors but the clerical factor doesn't change a thing it very doesn't change with these things do numbers just a number Our still has the effect of removing a particle X Prize and making your was a massacre and other matters terms which is just M Square if I square also it is far like these 10 here it's also something which absorbed limits of particle episode point you could represent only represented by saying a particle comes in and square or a particle comes in an article grows How would at the same point incomes known about sold this mess and squared X squared it doesn't over particle around it just absorbed and readmitted absorbs or just count particles it just houses a particle where are but strictly speaking it absorbs a particle and emitted from the same point Sierra bets 3 nature of these Lester that we all of course drawing diagrams these diagrams are really nothing refined diagrams were not going to growing that of finding Bagram argued struck ropes Lumberport beware within a girl cost is important to really understand major particle physics but Our just your straight 1 more will find bad more diagrams describing particle process this important 1 this is the basic process requires electrodynamics quite elected dynamics described reserve was descriptions of electrons and photons electrons and photons electrons described by the Dirac field but 1st of all the Dirac field for electron is composed of creation of our fighters grouper itself composed only out of annihilation operators is composed of annihilation operators so let's write it as C C minus but elite expression 1st sign there's a Osama all the possible momentum in Arreola possible moment properties Of the electron in particular there are annihilation operators for particles with positive energy by way of an also annihilation operators of particles of negative energy member of the Dirac equation solutions were both positive energy negative energy and there are annihilation operators sigh of positive energy and familiar would you sigh dagger has creation operators to off also positive energy Darren Havel krameri Rivera tree just sort of Dirac equation averages Dirac fielders creation operated annihilation now we do will switch this is annihilation operated particles from electron of negative energy removed apart removed I'm a lecture on of negative energy actually quote removing particle of negative energy is putting in a heading of particle of any of it that particle of possible removal of a particle of negative energy is the same as In addition Arvind ntype particles positive that suing the Dirac sea sort of thing and so forth and so yes
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operator over here the annihilation operated for particle negative Jacoby real labeled it can be real labeled as a creation operator uh foreign aid in particle both positive energy indicate Merrill grabbed reserves from a white car and this is from positron progress of Dirac field contains annihilation operators for electrons creation operators part likewise sigh contained creation operators for electrons end annihilation operating for positrons but Justice switch of terminology a switch of notation on to represent the fact that very positron the hole in the negative energy electrons is not strike and what the basic interaction of corn the dynamics of the basic interactional quantum electrodynamics balls sigh Baghdad sorry and a 4 . 3 before upon field is electromagnetic field the vector potential of a fourpart if you want a things incorrectly the vector potential abuse a Iong is affected and Sony Divakaran next then we have to make our vector outside we do that with Dirac matrices here where are we forthright correctly if sorry prior prime component to avert potential a Norwalk plus strike Baghdad Alpha sorry kind space component of the magnetic field was a cynical 80 if they had call 8 is just the field operated for 4 part which is the field operator for for cartons photons of course our articles which have a directionality polarization of polarization of vector so photons have in addition to a position and the momentum or a moment they have our little orientation a carrier will flag with them which points in a certain direction polarization and was will but that character of em and that's what those victories it's just a polarization of the photons are what does is don't miss absorbs electron but say absorbs an electron it can be made at positron unlike electrodes this 1 part this war sigh beggar time so I can absorb an electron in really electron and the same kind in your vote card that Ali but to lure branches of nor grand jury young it is a scalar OK so let's what's go back through direct equation you could make scalar by multiplying vectors together with letter now he makes galas for example a multiplying vectors right given vectors being you and a New York America scary like so if yachts votes now that we have a new bar we don't have a vector composer of side but we do of effect the compulsory size we play with the vector composed of the size it's just outside dagger side the prime component of the parents dagger Alpha sorry is years based on started right so sigh mega sorry if multiply by Prime component inside Baghdad office argued more acquired by the space above together ceramics a scalar mixed scalar and birth How do you want to use the ghetto nor nor was it a herd arenas creation my wish robbery full so we have years news products of creation and creation the army creation operators for electrons and annihilation operators positrons a use annihilation operators for electrons and creation operators positrons and he is creation and annihilation operators for so described a whole variety of different kinds of prophecies withdraw some all variety of different kinds of Russia's use the which electrons positrons is so for or creative for example they can take an incoming electron of a little arrow on electron show were short emotion and scattered in uniform cars or summer annihilation operated for electron creation operative of electrons creation operator for the 4 cars as service I would also have electron comes in quite trying goes out absorbed by the electrons his initial photon is absorption it was Korea we can errors were forced was electron electron electron or what we can also have electron countries gimme composite from him Our reminders electron negatively charged particle Courtney Martinez here we can have an electron coming in and positron firming and has usually drawn in this way electron coming in his drawing were narrow awkward a positron coming in this draw
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arrows downward and then if you draw it that way it looks electron just turns around but it's not really a really what's going on what's going on as electrons coming in and positrons communion photon off that's another thing that's contain E In this combination when you multiply side time site more Oreos are trying positron
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being produced by a 4 part all these various processes are contained in this 1 single expression here sigh beg aside from they all have the same coefficient of drag same numerical coefficient of from the assault always past the probability for the amplitude of the corner mechanical amplitude for them are all related to each other simply by a factor of the coefficient of a numerical value whatever happens to base was happen to be the commerical coefficient of setting right now which should where North constant close it's just electric charge of electrons young focus was electric charge electron electric charge on particle is basically be amplitude square square root of probability that an electron wanted scatters electron every point along its trajectory commit 4 times the probability per unit time along with trajectory for default art is probability is a square of electric shock so electric charges a square root of the probability amplitude for video for before can't be there part of that there's not bull reply not so drug series out bloated that's a probability of per unit there are far it's a dimensionless that's actually a dimensionless quantity to Burma corporate on an example of an example would be an electron bangs and for all to stop stop there was the probability that a for was a probability that its energy or its momentum its energy goes off of ours are far apart question now a electron of a given energy plows and a wall is Scott said what's a probability that momentum continues in the form of a 4 hour before and wraps elected the squalor of electric charge so that selenium electric charge In on quantum mechanics and classical field theory it's just the coefficient in front of the year interactive you are Her amid rumors if at work the yields for electric charge were defined by people who aren't How much current goes or wire this this sort of thing that sort of thing in microscopic quantum mechanics we usually defined electric charge of dimensionless where are we don't measure in terms of call loans we measured just in terms of recharge of an electron in units of the charge of electrons Our source that cancerous but really what is it's the dimensions probability that a particle which collides with a wall in 4 there are no real use dimension we always dimensions that you really need in physics on mass slaying are affected only yearly dimensions you work end of dimensionless units for everything plot units called on Europe to prevention and plunk you everything from Inc. of your house is leasing on Johnson more did well I sometime right several times with both process the full amount body which left him right that white charms on more and more stuff on missile that is that it is more of a turnaround now brush on the this time set has not nor not these basic fundamental process None of the process are paid me these are operators are all evaluated the same space time point but open or they start pouring which means the electron is absorbed related and photons emitted from Veracruz and poor villagers if those same EU head if I serve twice a and is really at full yes such draw yacht various conserved quantities here would include charge for example members because of armed In fact the conservation of is nothing but the continuity of these arrows if we had a process for this that would be war with be that would be an electron coming in a positron going out over the probability of a negative charge turned positive so if we represent a floor of charged by Mr. Harel here then an electron warming vertically upward time was up for the course electron would be represented by an going up a positron would be represented by a narrow going down are we do not allow arrows to come get from together the rule was always through ongoing arrows arrows contained in or out men go out khomeini goal
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our matter is paragraph conservation draws the consummation of charge is also insurance by a V on Our factor we 1 sorry in 1 side dagger assigned by either creates electron or annihilator positron that means over Burma civil society and not a awaits an electron the sigh and annihilate an electron will creates apart Nina case it increases the charge by 1 unit went on annihilate electron that increases the charge were Berwyn your where creates a positron increases the Triborough warn your site better does the opposite so slight increases the choice by 1 unit site dagger decreases the charge 1 so whatever this truly you govern where process to use conserve or if a lot crime is a lot of yeah do you know what I have read novels there's also the currency like this which government photon of the Dirac equation these are the interaction yes they have over the interaction I have Bob Wright the euro recorder that he said Pierre like it he said this task is not Iraq right has been will part your when you have loss look at all that bad it purchased shoe store but it is a unit of a mile right the Rivera His kinetic energy of the field of potential energy field Mr. are these spatial gradients are generalization of kinetic energy kinetic energy means proportional square of time gurus potential energy not nor the direct sorrow that's exactly where is here not right to sustain inquiry can now miracle nor a the quantum mechanical around you much more fundamental classical can use the quantum mechanical systems described by some Lagrangian and then newly amid a large numbers of quiet there you work out of classical behavior b a remarkable property here is that it this kind of acknowledging governs the quantum mechanics who will you go a large number of quanta it will also governed classical quick and past obvious their true as far as as how physicist find out what will grind you the Lagrangian systems are well Of course sometimes they get them on the basis of our people and sometimes they get a right and they don't get right by we know of course we will grant you know who our Kwong elected by Mamet's with extreme precision we Grand over the standard model particle physics with extreme precision latterly knowledge with North from Express were not by colliding particles together and working out just what kinds of basic interactions takes the described those interactions between particles Soros over on their for you don't quite particles together and see what comes out you are looking for you directly got a text of rotate community drop rotating means a rock star there were some renown left about the possibility that firms from electron and positron could come together and a photon also be absorbed standpoint say they will use legs of Britain or 1st Baron and of our quite remarkable there there 1 simple pride and describe we be part of a NATO did full form a shot electron on results not our worldclass now several elected back assured you our energy conservation derivable by degrading such prophecies all of all kinds of America when we integrated him with such a process all over time we found energy conservation we integrate over space we found momentum conservation this is the basic process it we talk that processed and calculated the amplitude for integrated all war places where process could happen that integration would ensure energy and momentum would be conserved energy momentum is concerned this career thing can't really happened we can really happened because would violate the conservation of energy and 0 River will more work to do after we written down diagram expressed an amplitude for it we have the integrated oval everywhere with
1:01:51
equal probability and that makes your human a call for a lot of thought that if a I'm excluded wedding so soon so where OSI they are closely it's good that uh army near our asked last year was dressed up after Asian annihilation up her it Marshall was no you don't take look a good question member of you don't think a derivative of the creation operator the field looks like some integrals are creation operators or annihilation operators with things like eatery IKX Ito minor fire may be right in different cities not these these things don't depend on provisions young no I can't no I Constancia's ordered differentiating these objects here us why pull down factors of cane or make a difference look premier a merger or some other examples of interactions other kinds of processes which exist in nature which could be described by this kind of field hearings are protons neutrons and resolve protons neutrons and on former system which is fairly similar the quantum electrodynamics somewhere in the spirit protons offer Leon neutrons affirm Young's that describe exactly the same kind of feels Adams electrons so it's good name sigh Proton sigh neutrons and then the other objects in the theory are less on pioneers on an interesting courtroom on of climbers on they are I'll rules learning as we go on the air quarter by quark PARIS without just 2 hours so it's just think of articles on their scalar particles these arms Dirac particles and pine arms scalar particles become 3 varieties plus miners and pies hero was a plus minus 0 electric charge electric charge Park pluses plus 1 unit 1 unit in units electron electrons charges forms negatively charged and this 1 electrically neutral protons positively charged the neutron is neutral so we do examples of some interaction which door car nature there was sigh dagger Proton outside proton sorry neutron what's in our neutral Our absorbs and neutron and creates a proton with Europe half pipe plus prime writers were to strike I miss absorbs a positively charged by Mozart and Arthur grab armor and absorb negatively charged planners are minors he Mitchell neutrons absorbs fraud on forever right shore of the neutrons and from our from time and does not look possible because it looks like a negative charge were positive charge for a coop pipe plus this 1 interaction which occurs in nuclear physics is 1 interaction which occurs between on and nuclear arms nuclear arms a Procomm neutrons described like this of course is not really fundamental interactions the real things quarks and we're gonna break this down a process seized in terms of quarks quarks and when we didn't know about quirks we represent protons and neutrons in terms of fundamental fields climbers on the terms of from the rebel field will write about things like wealth from Belia beggar neutron side protons and Heidi minus this absorbed but storms of pine minus and the probe tartan Jews often neutron em that protons side protons 0 and also strike neutron starring neutron you're aware they think described described Proton crossed the neutron plus a pipe plus but of course this vertex here describes a process to use it however want describes protons in indict neutron and by neutrons and neutron represents our bar emitting a pipe last although right you could push the legs often down when a leg this switch you have to to replace Miami articles of again outgoing neutron and take that out going to charm switch around broke communes becomes an ant by neutrons coming near the outgoing neutron when switched around upside down becomes an incoming and try so his incoming Proton incoming and
1:08:38
neutron annihilate each other create positively charged partners are for Gao for all the different interactions take place between proton pine and neutrons and basically all of them can happen as because charge as long as it considers charge it all happened all part of nuclear physics all possibilities and their codified in a small number of Turner's side of protons and neutrons pipe plus so forth so that's another example of where the hour with this technology woes important to the early days before you quarks from the fact of the proton and neutron on made up about quarks well the size of these accord caught distributions like Adams electrons going around them and so forth but much much more it's much much more for and because the smaller means at some level you could think of it as a point particle words were all our measurements interactions and so forth don't break it up which don't break up brokers are you could think of proton is pretty much a point particle and that approximation you pretend protons and neutrons described by fundamental fields of course for happen if you hit the proton neutron hard is break up our rules break up Court and a breakup of the quarks and you do you won't get you won't get away with descriptions with from prescribe support for your you have to remember me quite right arm has a a a a a a a a a a electrons from bigger or rocket are yacht the other is of course another vertex in involving protons protects involving protons also involves folk hero do about protons neutrons and pointers on but be because protons are charged with of other attacks proton folk art program you can have proton goes trial for conduct was surcharge of proton goes the proton car is allows brushes and also electron grows electronic and for Carnival out processed soul possible process that take place when NATO proton encounters an electron is proton can antielectron absorber for cars now we haven't talked about building up more complicated process building more complicated process to use but you didn't see the pattern you could build prophecies as elementary units the elementary units are vertices and you go up what do they call off that this is profit not described point Mueller said start with described by a grand jury this corresponds to a probable grungy in 2 different point sewer grungy and some basic unit of interaction which tells you that a proton is absorbed in the middle of a point and the photons as the interaction of saga approach from for upon and reduce as required Radick terms which moved before Parliament memory with things which move the photon along from pointtopoint they can act many many times will the photon from restorer and then the photon can be absorbed over here uh we're not there were clearly variety of this sense from 1st principles and is telling you that these basic elementary process Out of which you build everything are codified in the year granted were grind you always describes things which take place point or perhaps a pair of neighboring point took terms of arrived here is they are this 1 he described as being an 8 point something comes in something goes out from standpoint the other chosen gradually involved derivatives and they correspond with things at very close by neighboring points most of particle from 1 . are no action of the distance quantum field theory and worst there or not at worst a good thing but you could move from 1 point toward very very infinite test close point water you cannot process taking place at a specific individual point I don't know things in what once you would think of particles from 1 point put them both processes are built stock car broke off our more elementary process to use in this case something taking place at this point from big taking place at this point and then I'll large number of will process moving New York from whom I see it as there is 1 of those what I want your very movie and has been reverted say is that it is not turned
1:15:02
would crime will prompt shut this process is described by a large number of basic human a large number of basic unit is a process taking place at this point that sigh dagger contract strive for a pardon Mr. and then the basic elementary processes series which mold the particle from 1 . 4 neighboring point toward neighboring point and then be brought before a dollar a day in the long life he easily do each individual processes and were granted but you have the compound them together May God can't handle more won't you're lunging compact a a number of times different member or rising in itself is made up of fields fields on May the creation of annihilation operators a grudging at each point of space next point space that point what and build whole process so Grosjean is not something which is a fine or it describes the basic unit an element that the compound themselves together but prop exact reviews warm I'm just bond axis cost I wish I stressed how he wrote came to all were also due rural roads live up to were you you're out of here or there will be as low as this past was and your whole life that fossils Arthur on our house for a close eye on glass is is high and is tossed were a few hours which shop operators operators which make process have her capacity the basic across a series of basic elementary processes the absorber particle emitter particle forward your absorbent take it in a onepoint River that take it in a 1 . org spirit out from the standpoint multiplying fields together could bring in 1 particle and spit out of 1 on here was proposed by a single field by itself can absorb a particle 4 spit out of particles the product of 2 field can absorb a particle and spit out particle nor was there difference between Our who warned case I feel a single power before you absorb the article or article tho powers move for you absorb ended half a stress that it is not home just the code of the Cold War for the elementary process a big firms was based pardon bring in terms of space time ex ante when you think of the trajectory of particle is being built by car or of particle as being built up and many little steps cost without the legal limits Whitacre limits by replacing the reviews of differences by derivatives and so forth but let's think about differences rather than we break up the trajectory I will pieces and then a particle is absorbed at this point remittance this point solids jumped from 1 . space time to report the and it's a job at this point again and removed and remove this point in the process at half from point to point to point for now are you In limits that we subdivide this trajectory into an infinitely small series of steps the number of prostitutes goes toward affinity pipes limits involved with the simplest way to think about it is the subdivided everything in little pieces and think of Basic Element the units of emotion from 1 . 4 neighbors point so that the way to think about and fact quantum field theory really always does have to to be defined by dividing up space time we sailed out so we really defined break up and allots a little self but having broken up and the 1 now at her with it's not a coach
1:21:20
what do not start now or letters now I was struck fast suit last our she 5 funding Molson movie tonight now that it is not a word is all that is rabble automatic you were were granted dealers Everything will be low rents and all of that kind of thing about our relations 0 4 will be automatic have worry about they are not sure exactly what question you're asking so came here also at a parcel bomb Scott Roeder zoos will have as a Stowe at home a connection between creation annihilation and Heisenberg are Heisenberg uncertainty another way of saying you even describe things In terms of position or moment my box right yet In terms of creation and annihilation operators creation operators annihilation operators Our either the functions of position or functions of moment of turned from the field operator so X is the creation operator for particle at point X is made up of our or field operators for years which are functions of momentum and so creation operators or I had creation operators for a particle moment he or creation operators from particle moment of position acts but they are not creation operatives for particles provision acts and momentum we never have operators which create particles of momentum p at position acts I don't function of X the functions of peat and the relationship between the function of X in the functions of is simply Fourier transform Fourier transforms the essence of the uncertainty principle there were said car is close the builder function which is localized positions you have for use a lot movement to build a function which is localized movement are well it's going to be spread over acts but this is just exactly the same thing as it is an ordinary alone would require mechanic Are you either have something which is a function of X or a function of PU nothing which is a function of X and for so Kyoto I'm so by the X T Is it so Mr. it OK at some level would not different from what you do and classical physics in classical physics how he defined derivatives you divine derivative by dividing up space for little cells and define differences that sort of derivatives now in classical physics you couldn't really just take a limit rather smoothly and forget the fact that originated from very discreet picture in quantum field theory more problematic you really do have defined the theory from the beginning by dividing up space roof 12 and having provided owls in each cell the field operator was now not a function of continuous positions it's now functional which worries during the river's becomes differences and that of the quadratic Hamiltonian pickup particle from 1 cell more that's what we White rooms but would not to start right if fight is 1st of lighting up space placing your field operators warned or however many cell and then the basic quadratic interactions will absorb a particle from 1 cell and put into a neighboring then indeed you would pick a limit we take cells to be fairly small and solo In terms of a discrete picture a process that might absorb electron over here the electron which happened come from a neighboring cells so for sure try came from a neighboring cells absorber over here amid over here and photon then photon Top from cell to cell to cell quadratic
1:27:36
also the electrons or half of the about the electron for carnal hop from shelters sales were mind from what charm grow
1:27:49
so if physically took kinds of 3 hopping from Aug . Yarborough and interaction which absorb some particles with them from the same point in the early and the match turned here and square miles squared it can be thought of as a kind of interaction were a particle comms Inter with cell and news from with a court square if were a sign of how close string 5 0 0 very precisely for years but quantum field theory is kind of a limited a discreet period which motion is replaced by hopping which is saw of a product all you want that is basic probabilistic played tinge probability that were full of this to go you have to have something going from year to year they're not as opposed to is not find me how Ms. Mitchell was based on the law so that you saw what I have heard cross for a year while passes E mom had she not army areas not to sue is slated to cure small that John Ireland a sign them or was it was too soon the plant Otto a a half the position of the filament field operator operates which creates Sowerby Michelin final conditions be absorbed initial initial conditions are simply the start of the start of a particles communion and that happens that whatever the source of the particles sources R B final conditions are just described by way of the detectors our sewer and in each case creation operators offfield operators located at the point of the filaments which create a hot electrons described the emission of electrons from points and the absorption of electrons are also described by field operatives at which say they can to stop you're not just the prime there's yeah that's right that's right you described as a historic start the easy way think about to start with a vacuum now in this state is not back in the initial status on particles produced by the year by year filaments or whatever the source of particles are so those you represent by a bunch of creation operators or field operators of the position of the year of the your sources sign as the initial state the final states or for evacuees and and annihilation operators endorsed beggars bears various rap and then stuffed takes place in between these are just the initial and final states but what goes on in between is determined by will grounds what goes on in between revival of Rodgers so you might put many factors of all grungy here I each factor of a might absorber particles and made a particle in neighboring point were not how was over Iran's you here you could pick although particles and them simultaneously from 1 point to another reabsorb mystery starting point would be some particles which were produced over here that would be a final friend were final states might be particles and absorbed all what happens in between is governed by the dynamics which is just were Granzien repeatedly acting and taking particles from 1 point to another creating annihilating particles that at the end of a house how are so how they say Will really all this is off fleet the Israel's position I do find new reference explain exactly how you beat point Maine point for us is the interactions with basic interactions on coded in simple expressions involving field operatives reasonable going there is because that makes
1:34:15
it very easy to think about symmetries for example of this terminal a grungy and has a cemetery was cemetery we talked about before the symmetry is the symmetry of multiplying society by each of the RIA times they know where they can be anything sigh dagger at the same time multiplied by means a minus I made a slight curbside beggar will be on affected by this she the governor of buyers changes sigh so it is a symmetry symmetry of the program is multiplying sigh by a phase multiplying sigh bagger by complex conjugate trees and doing nothing that will not change a sobriety and that becomes a cemetery where symmetry associated with was just associate with the statement that you have an equal number of size and fight back if you had different numbers of size inside Eggers this would have been there was a symmetry that has to do with equal number of sizes daggers charge conservation so what supporters of these basic utility of this the past will be to write down expression were weakened reel off symmetries and from the symmetries read off conservation laws that's really what this is all about the symmetries the conservation laws and very very basic go primitive processes which take place at each point of space time as rapport granting contained what do you do when it volume multiplied together many many times which is just the the same as saying you repeat basic process in any water that why would any think it can happen that allowed the happened by conservation laws and all of that is described by picking the foreground just hitting hitting hitting hitting so it take initial state and eventually evolved into the finals that was the Alcoa of this is an attempt to buy that I had with those governed by find rules which were Mike and pick up now in any case our would probably will at some point but tonight all I really wanted to do was to show on show you how basic processors use coded Are you a grungy dear will use that to see how symmetries and conservation laws are connected with much Chateau a loser world because the South the jury let's take a case of the electromagnetic field the Eigen values of the majority of electric field or are few operated in general on the possible miserable values of the field with our you do measure electromagnetic fields there were numerous measures how measure or field electric field work for your charged particle and the words to Howard would you be given value every eigenvalue how head elected field field operators general are built by about creation of annihilation operators creation and annihilation operators don't commute with each other that means in general the field operators commute with each other well what so what's not the commute fire has the canoe with ficus same what's commutator between a thing in itself 0 always commutator of fire with itself was always 0 had because you configure calmly paid out fire at 1 point with fire another point and neighboring or some other point of view a different point of view neighboring pouring each 1 of those Pfizer's made out of creation and annihilation operators it not the same operators because the value different positions a space of but in general they will not commute where the meaning of the meaning of this is that in general you cannot simultaneously measure of the field operated with 2 different positions there on certainty relations in measuring field what kind of derivatives a few 2 different positions a spacetime store U.S. rebound think let me about that U.S. yet U.S. feel operator big richer arm which could be measured well yes the fuel operators could be measured they're eigenvectors Amargon eigenvalues play the usual role in quantum mechanics and the commutation relations How you limitations on being able to careers souls in the rules of 1 . 4 4 just over a year to the edge of your career to both Irish who to hold both to the not less Kuwait about nor bigger bombs be are you thinking about her be better off majoring in terms of number of all kinds and there were that it's not profitable to of electromagnetic field were you thinking about microscopic physics and born vaults leaders but could also brought up for you you are nonetheless I got shed a shit was such as those lights lawyers how we used say you have the brought us this is a volley over processes could repeat warned the next next words were you could have a process of that process of our prices of processed basic all processes of both about a basic element and basic elements have 1 important feature that they are associated with points of space or a neighboring points of based neighboring points space critical get so vast array of saying their local and nothing America's nor action the districts basic indivisible prophecies of local and nonlocal process to use but 2 of the 4 . go were birds not a boo we'll reach for and then move profit Evelyn Roger that you think about it a simple decision by happy many of them he later transformation address also that they get the city of David as generation of movement and the auto destruct roughly speaking roughly speaking simply exact you pick 1 who off with scored the euro interaction grungy know interactions have point X and you multiply together at all points was based X warned X 2 X 3 X forms of Audi get while 1st or you just get 1 that's
1:43:17
not interesting doesn't do anything and then you get although Powell possible terms in which every factor here is worn except 1 except 1 factor that will give you the some mom who grungy and oval or space Richard Yuri Occoquan plus forward Ryan 0 . X the same thing a point X prime 1 plus 4 Grand Union Point X Prize warned cost or grant point X double crime knew this every point space the point of space means every point on great let's take just 2 terms were just 2 factors was a give your gives you 1 class at point ex post bail at point X prime plaster L at point X Prize however point prime right was as represent rose from nothing happening this represents a basic for example basic interaction of point this represents the same basic interaction taking place at a point X prime so it could be nothing this could be particles absorbed the middle point X this could be particles absorbed report X prime and were about this 1 all right so Ms. Kirby something else happening over here and this won't were represent particle and absorb the point x something Ltd there is a 1st and then this is not the 1st time you just represents 1 profit and only 1 last says that something is contingent on something else and must both 1 the that represents 2 particles being absorbed cargo and 2 particles you don't you hand them eventually by the time you multiplier woollystemmed together you get an infinite number of terms in which a basic unit can happen at every point of space once and then and the number of terms where 2 points of space are involved in relief a number of terms with 3 points space strong with 3 . 8 involved the particles particle those our another particle goes out the particle that's only 2 points of a space time and then another protects over here so as to particles you'd report out every week is saying is that if you have a motion of former although enthusiast since you since you have motioned her emotions movement from on for for a finite distance 18 incident number of applications quandary worth rule Lucy was viewed as long they well I kind of had of motion that part of donkey and trace how social emotional particles from here and here we are burned this trend will appear this term here In this big proper somewhere isn't as big product there will be are which involves . 1 points with the neighboring point with the neighboring . of the labor point which will transport particle from here so some ways in this big product you'll find exactly the right thing to take you from here to here actually by many reports many foresaw will many many such terms which could take a particle from here he depending on the orbit the actual amplitude to go from here to here is the sum of all possible ways you go from here a year by multiplying airforce Wong stringed of factors will give you are possible prop possible process whereby we particle could grow from this point of his point the twoyear overhaul local amplitude thing you square to get a probability will be the the samples all if it is not so warn you multiply out big string of terms you will find arm is corresponding all possible routes from here to here the amplitude will be the sum of all those ways of getting from here to there when you square it will be you and depicted were part of their a plot to attack they say they got a guy that creditors to try to trick to go on really comes for you have the Grover but you could just think of it as a trick right combinations your and that's the that's what really is all about all possible combinations are Our ways of going from 1 place to another are described by this product here I'm CD what I found was really more pepper Gore expression but this is a list of the chief a toe well I quantum mechanics it's not the principles yet stationary Cheever yah Of the principle of North not the principal of station its classical mechanics the principle of stationary action picks out a particular trajectory picks up the trajectory with similar action this is the principle of summing over trajectories where are you with amp approved some the fight back a 1st moviegoing has nowhere you from down my office To mark for me the figure our what the what the Lagrangian want you Lagrangian rules of straw show it does it does it was only like any other mathematics I have taught you have be clever Leon New World Two moderate Corker warned you don't know what you're doing you groping in you and there you are are on the art form finding tricks 3rd to figure out what below you years from experimental data once you know it use it very very precise former was to calculate how chief the resistance nor somebody tells you years grungy here is a process I'm interested and 2 particles in the fall particles our 2 particles common from here particles go over here calculate for me probability for that process perhaps then heard quite a few is extremely precise toll was no ambiguities how uses the ambiguities the
1:52:18
ambiguities of the art forms of figuring out what that Lagrangian is from experimental data yes of course was part of the a crime stretched to drag after big before the before the big book all around you I had OK I think what you're asking me is how complicated grandeur view of the world are is what at least and physicist minds there is 1 of Grand Union which governs everything now that may may not really be true but let's opposes any contains a large number of fuel to contains all of the field describe all the particles in all of the interaction and may have the son of many many terms like describing lots and lots of different interaction but with 1 will grant you are maybe composed of some of pieces which individually look like a recognizable pieces but the whole thing is 1 big will grant governs all of nature of this baby really falls but that's the idea is 1 big run June with many terms as governor everything you've got their warned while yelled maybe a little better than 1 time roughly speaking yes every time we discover new particle we discover a new field that has to go with the Lagrangian every time we discover and the process that New interaction program here on so you might say it world this whole thing is a big giant mess and indeed it is about their probably at least a hundred different elementary particles things we call on the particles Olaf 500 different terms of grungy and in fact so bad the kinds of programs use of people right down to describe standard if you if you want to right down all the physics which is not which means choir mark for dynamic of the strong direct strong nuclear force on Cromwell dynamics a weak interactions on our gravity and everything else you will grant you would fill a book I don't think but with a couple of a couple of closely spaced pages pages that ETA a for care Shea Clark Galilee can and well on the you going into a new going beyond basic corn you talk there were rose rims which rim group or a class photo call the court missions will grow you so for example here's a coupling constant but may ask the man's squared is also a kind of coupling constant our also coefficient and were Lagrangian various coefficient to grab a bite before a fight of the 6 5 0 0 500 each 1 would be a cop so at some next to big mess but wants you know who were burned here you know a lot you produce a lot of different kinds of processes that have you have to know the whole thing in order for example the study quantum electrodynamics well if you want to do with the infinite precision you would have to know how the electron interacts with particles all different kinds of particles from all the possible interactions but in fact fallen works I'm not very important away electrons b quarks up pretty much isolated from electron don't those they don't mix to march with them sitcom pretty much ignore quirks if you're only interested electrons and photons a comic energies you just don't have enough energy director of cents the kind of quirk structure and so for practical purposes you could often break off a piece of this program and to all the other things is not terribly important per worker calculating break off small pieces were burned you calculator work but in principle off you wanted infinitely precise things about photons electrons you would just be the whole thing this is not a pretty picture this is this is really not a pretty picture of the euro very much makes you feel a quantum field theory of some effective description calmly and from Hong biker hydrodynamics or any other effective descriptions which is coming from some more fundamental physics and just what's the right turn around effectively describing things at coarsegrained level that can't quite a few theories probably just of coarsegrained description From remorse for mental them there as long as that's the case can be very very complicated for a group not yet I got a bill is also what the what's officially called the spin it will be I a set out predictably are you commit gravity who's been the bomber who grabbed he of us out of here general Motors to know this will be mine she general Wikinews does not think in general and special relativity young this is this was the condom additional course can refer workers a toe all got except from Morgan said what just terms were which attracted then at a bar John showcase tour Mobutu I think we talk about this before Morocco you again so we see that what a mess Turner's the coefficient of fire squares are supposing we had another field about called and supposing you look around you and I have no words H 5 square now let's not quadratic Cuba's source described described quite unify our and age being emitted down that's what termed as right now Nigel was more terms something like a VER which now V is potential energy potential energy is the potential and you feel suppose a video of age happens to be a function which Vauxhall would say something like here each via is such that the minimum of the potential is not at age equals 0 the minimum of potential energy defines a stable equilibrium points at vacuum as a stable equilibrium point tho and for this particular potentially might be Short Minamata and real vacuum would be chosen to be 1 of these 2 men this letter has a nonzero value of AD each so this vertex there be Collins just maybe it's not the vacuum value of HEU just becomes a number in the vacuum then translates into video the year your job a left theater the war but young corpse bring your definitely for more please
2:01:48
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Metadaten
Formale Metadaten
Titel  New Revolutions in Particle Physics: Basic Concepts  Lecture 9 
Serientitel  Lecture Collection  Particle Physics: Basic Concepts 
Teil  9 
Anzahl der Teile  10 
Autor 
Susskind, Leonard

Lizenz 
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DOI  10.5446/15067 
Herausgeber  Stanford University 
Erscheinungsjahr  2010 
Sprache  Englisch 
Produktionsjahr  2009 
Inhaltliche Metadaten
Fachgebiet  Physik 
Abstract  (December 1, 2009) Leonard Susskind discusses the equations of motion of fields containing particles and quantum field theory, and shows how basic processes are coded by a Lagrangian. 