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New Revolutions in Particle Physics: Basic Concepts  Lecture 5
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Stecher University the
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Bosnian phase velocity OK that pilots let's talk about that Romney generally the phase velocity of relieved doesn't have anything to do with measurable properties the wave of or all of the measure of the things in quantum mechanics visible ferocity which is really be velocity at which signals move the velocity in which particles moved so far but so a show you what's at stake what's going on on the 1st thing is to have a plane wave signed a cosigner IKX and that's oldest equally IKX for 22 like a acts minors on May Get T
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adjust sign is a sign of X might make fuel also do in fact purchase right that fine FKX firms from can also like that and how does that wave move out the pop of each class moved top of each crest moves are in such a way that this thing inside the sign is constant and goods for example right away he at time people 0 0 Mexico 0 the sine wave Oliver signed waiver was maximum of 4 of x equals people's sign with happens to be here OK then how is the sine wave after a certain amount of currency it the place or that point he has moved and moved to the place where X murderers or is equal to 0 with that that's at the position X is equal to or may go over Katie times state riding bike Katie surprising if you think about 4 minutes on a is a frequency so In the period of oscillation kind of oscillation it's from all of the kind of of oscillations of the Pioneer but the 2 parties putin bowls and so on dish is like 1 the parody of the wave will exceed the amount of time that takes where tossed and Kenny was like a 1 Overland there actually took pies in these equations Tobye's innumerate would women and so on Kerry what Oh my God overcame homemade Cheney is land over it's a relatively divided by the Kelly for wavelength is distance of the oscillation period the kind that make the ratio the velocity so this the velocity Our the peak of each wave of trade for a plane wave that call the phase velocity was center throwing away from shore players have a connection between on Omega and Katie it connection is remembered only laughter remember is that Omega is really secretly Energy Inc 8 Israeli secretly momentum if we said it probably not and so using the formula that energy is equal to momentum square divided by just becomes all make square physical decay square provided by 2 am rising momentum squared the match twice as fast as usual with age particles Siegel's wand and factors no season formula but last bars a case of Alitalia for example lets computer the phase velocity the phase velocity on shorting the way of patrolling live on Omega Omega is equal to carry square over to Omega square squares Omega His case quit over 2 m so that is the global varsity its Omega divided by Katie Get provided by Katie physical decay only tool and that's phase velocity K divided by 2 AM what's the velocity of a particle in terms of its momentum momentum divided by him as extra factor to hear what's it going there peculiar playing the phase 1 of the things velocity is not the velocity of the motion of classical particle OK let's just keep that in mind it's true that lets the something that's now surpassing I a constant the frequency of every way I simply take the frequency of every way all of them all Katie and I had the same constant I'll watch other call I can't confirm and name for it it's MC Square but that's not the resource for but just a and at constant almost all constant the frequency of always what those that who could be group Ross the Phillies velocity well it changes it on the radio the violence by Katie will now have the extra Turner lot of extra tournament will be the same does silver carry knowhow next terminate the phase velocity will change but tell you right now there is no physics is just a letting a constant the frequency of every throwing away a correspond to corresponds getting a constant energy of a particle and ending a numerical constant energy doesn't have to change anything on only energy differences a river report by police see what's going on in terms of assuring away while assuring the feel of society it is some kind of some of the road summary of our creation operators arrived annihilation operators in this case Vitaly I. K X E miners Omega well it is the only bigger which is related to case so Trevor wig of Kerry gossip opposing a plant lawmaker just as constancy she wasn't do it England In all multiplies in each 1 of these waves he said we are see sorry remind ICT although the In here that make up the shorting the field although multiplied by the same time dependent phase he so does as if you have a solution of the assuring requires a New England a constant phase it would just change the solution say sigh of ex ante it would just multiplied by of minors I see as what I would do it would multiply the live side by side representation would change the way by multiplying it by a timedependent face all of the quantities of physical interest that I need out of the floating the few involves signed times its complex conjugate the probability density for example times I start or a possible expectation values quantum mechanical expectation values all those involved sigh and its complex conjugate so happens the site and its complex conjugate when you perform this operation it cancels out it cancels out because sigh Stogner gets multiplied by each of the past I CT multiply cancel out as a consequence there is not physical measurability heading a constant the faces and never unless it changes the velocity Of the shouting away so there must be something about this change of varsity riches world's changer frequency would not on a let's say for the phase velocity phase velocity is not something which is ever measured when although ever Peters when you multiply site times start puts an artifact of a particular our mathematical arm circumvention of many in the group velocity really does mean some it is the motion of the waiver motion our if you have we will move packets our witches so in some places whenever you have a bunch of Williams which add up a bunch of awaited Wenger plane waves which is set up to
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something like that maybe it has oscillations but which would call Michelob the whole lot numbers with the varsity called the group velocity but let's see if we can see that the roughly why it in Tuckahoe bunch of plane waves rippling labels goes on forever as a possible they led them up so that you get a concentrated lumpsum the answer destructive interference right destructive interference so that those are being phased in a bed up here and out of and cancel or here so the question comes up if you're interested in the motion of and how it will use of slightly different frequency reinforce each other and make a high point of low points that let's stratified how that works let's take 20 not a single aware but that's the Of those in neighboring close moment momentum and try followup will be ridden 1st sink our constructive interference takes place that be good enough for us just follow aware of that constructive interference takes place between 2 some particular take eatery IKX idyllic we could just pick signed signs good sign chaos signed K X minus Omega of K I toured physicist over moving along with momentum can be energy omega unless it another of which is parentheses around signed a cable car line where Nikkei are very close whichever X minus on maker of Kate times feed where are they in phase and where they out of phase is means only in 1st each other I will say and indicator that it will mean that the 2 2 terms he said I have seen salaries and other places where opposite signs that 1 easy way to find out where they reinforce each other as they ask when Izzy argument argument meaning you like it here Wednesday argument that this way the same as the argument this way that those are the places In that case the particular place with none of this wave and the argument of this way it's good the waves will reinforce each other each other and they will be constructive interference that where's that that's the place we're Katie X miners Omega of Katie CD is equal to Cape Horn X minus Oh made that's just carmaker prime Amiga prime maker of Cape prime seat but outside this summer following what he came escape prime acts is equal to or go minus Omega prime moon will reinforce each other along a trajectory where X and are related by this equation I guess that's just divided by King might escape and will assume that take on a very close Rich other adjust the simplicity of the magic on that the only differ by a very small amount a small fractional amount then what Omega leader prime overcame an escape Prime but we don't have may go with respect to case that is the derivative of Omega with respect to to carry if Omega Omega primer near each other and says it is replaced with a mean 1st each other will travel on an order bit which is X is equal to the derivative of maker with respect to carry the BAR Omega by decay times Katie this is also a varsity it's varsity all over the place where the waves reinforce each other it is called the of velocity risible ferocity let's calculated if Omega case over when the plaster arbitrary constant Cyprus a phase velocity ladies What about the group velocity that's the derivative over Mega with respect to Cary derivative Omega were respected carry that's equal to divided title and otherwise known as Kayla and not year from here nothing Zetsche this is because this is a group velocity v Group among the things that grew velocity does not depending on us extra it is fitting that I couldn't reach frequency number 1 and number 2 it's exactly the velocity of nonrelativistic particle momentum divided by next summer the 2 to went away exactly a differentiated I got talk divided by told him and into an award for grant velocity is the thing which is most closely associated with the classical emotional article that's also the only thing that's associated with the propagation of signals and not the phase velocity we got heavily and moreover there so we want to and I could feel like he's a Bob so let's go that lets go through that and see what the series not the speed of light this is not like Let's go through that let's take a relativistic wait and calculate the group phase velocity that we need the dollar fact but 2 we need to build relationship between Rigby could start with the relationship between energy a moment life now but doesn't it doesn't it doesn't it but it's a good it's it was a good question on bed it doesn't have to do about it to separate must be aware of the face philosophy of life who lost all yet let us only give you an example of that happening right now on not guide with NATO uh Yao is we're not with practiced only equation for a particle with vast we begin will begin in order not to figure out the relational the wave equation is nothing but the relations between Omega carry and the wave equation just the relation between Omega and Katie flow a relativistic particle particle moving close to the speed of light which gun that's got message did not mess would move with a speed of white pocket what's the connection on regulators energy but that is 1st and the former we might remember best whatsoever between energy and momentum for a particle which is relativistic farmers however the relation with momentum Pete Square Square load of peace square pass em square but probably want to put the
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speed of light in year because of seat of what square but let's Siegel toward yacht with that 1 I'll move will allow it to put back are the seas if we want to its it's unnecessary if the energy and if we don't particle this is exactly the same as riding on May His eagled the square root of K square foot and squared for a relativistic wave of relativistic particle the frequency is the square root of case Quetta stems Greg it happens to be equal to role 0 and it's all bigger equals the magnitude of K apart from the speed of light they called 1 perhaps the relationship for a wave moving with the speed of light maybe it is equal to cash what's the group velocity was what 1st phase velocity officials velocity is Omega overcame a right these days is Omega over Kang and that's where I was at mean 1 of right right what about the growth velocity legal that's a duet of Omega with respect to that 1 of the ferocity and the phase velocity of the same with Messi equal to 0 right from forget his masses just that mayor of course bears our energy will square of momentum squared the match square but now that's calculate the grim ferocity when this is not equal to 0 what both of them what's calculate both on a can 3 phase velocity at the square root of K squared and squared off over can be but let's put it well inside the square root of all inside the square and it becomes case clip of case square drive is bigger than a small 1 the other 1 the presence good overcame square is bigger than 1 so the phase velocity from a Gaza Katie it is is bigger then 1 bigger than the speed of light and followed its still scared wave movie fest and the speed of light but what about the phase velocity that's work that our group velocity thank you regret velocity is the delivery make with respect to Cary the deliver the Omega with respect to Cary ropes struck filmmaker decay that take square that gives us 1 all twice the square root of case squared presume squared and then we have to differentiate the argument here with respect to case of that just give Katie users KOR visited directed at will it is also equaled the square root of K of case square send square as a man I the grant velocity squared of case quit the case with wasn't squared the phase velocities could make a square and sclerotic a square in most whichever is greater than 1 this 1 was always less than 1 that is what is less water and flak misuse of the velocity of the relativistic particle with momentum Kerry a square Thank you young distillates to each other that is it happens as was pointed out but somebody Ali product of the group velocity the group velocity and the phase velocity recalled a 1 served distinguishes of each other that someone accidentally very the greatest beat 1 1 such a freak wave cut that's life that's that's the case you will make it is equal or proportional love about OK that's the case will always have the same velocity crack was only In the case with all the lives of different frequency have the same velocity that the group phase velocity of the same that's a good approximation of authorizing opposite the approximation the sound of other things about a level is low frequency sound waves along with pretty much the same velocity and very the that's right but that's but much of a difference of these 2 kinds of velocities is connected with wave dispersion where there were the change fact where exchange checked absolutely absolutely OK so let's see that's the story about leaves us about the group velocity Faisal losses analysts said in quantum mechanics because they effective for example he had effectively shift in Omega is not ruler of physical effect whatever as an example of the fact that most times the phase velocity is irrelevant to real physical propagation of any signals any energy flow or anything like that probability flow the last so said that it can measure they face the loss of a Middle released at least for assuring graveyard for but therefore effects on the same that the saying that gets a lot more complicated when you have those kinds of disposed of materials are called upon to move but you know that abuser squats right now it is way yet Web what charm forward is it bomb spread out over time will use which always have the same velocity if different components of the way you have different velocities this could spread out right back so that if that's the case where gays and nonlinear function of Katie basically or maybe it is a linear function of Katie then the middle spread that's the case are always having won universal velocity looking at some point maybe if somebody comes back and asked me this question about light clones of things we could come back to it but it was a good question but it's not quite related to those he was also 1 of the building before getting to on yet on before get the let's discuss the issue of momentum conservation would discuss the issue of energy conservation and I you example was really just an example of our the kind translation and their parents also these include that go into a scattering classes and quantum field theory conserve energy firms remind you wear quickly and then show you how they energy count momentum conservation works very very similar we will come back to these things but that I wanna get aren't affinity Arturs that's what I wanna get to tonight
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let's get back with the good momentum conservation is really quickly other energy conservation work energy conservation we had for example some passes as now is a bunch of society creation operators
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Northwest sigh annihilation operators of regicide creation operators act on a state with a bunch of particles in it with momenta and then we calculate overlap with me in a product of the probability amplitude for a final studded with a bunch of other articles K. time above about these fields act on the initial states these fields act on a final states Of the lower on Monday ruled out what is supposedly although processes take place at the same point of space and time at 7 . the example that I gave was 1 in which 1 particle came in 1 particle went out and a key in scattered off a point in space integrated all all possible time for particle is they're not as particle but Studio B target was the author or times and so the article gathered at a time when every gets there and that's represented by integrating this all the time if you remember each 1 of these societies for each 1 of these size is made up of a bunch of things involving a is equally IKX each of minors I don't think it he says or maybe figures being the energies case being the moment that set off list of players the origin of spatial coordinates space coordinates then this is just a cold 1 Oh the operators I will finish calculating everything we only time independence in the amplitude comes from Ito the or I'll make it a little remind you it looked like it looked like he had miners I Omega of each around seeing need minors I Omega came to see that product that be initial states and then for the final states there was something similar each of the class major Kate following from of what tragedy the values somewhat as b out outgoing momentum and healer it's minus the sum of all only incoming Omega carried income in times the 1st step was to say we integrate the good all cartons representing the fact of the matter is at any time the will of this gives right into overtime the I got function of delta function of this summer the final moment minus the initial momentum said final energy use minus initial energy over time all we get is a direct the function all let's call it or they go I know final that the sum of all incoming energy at their energies minus the sum of all coming in the answer is you must incoming energies equal to the outgoing energies and this was just a consequence Of saying the the process could happen with equal probability at any time now what about momentum conservation momentum conservation is exactly the same sort of thing except that has to do with the space translation of a process can happen at any point of space with equal probability that the momentum conservative leaders with example 1 very simple example business a process which a pause convoluted and bullets In 2 particles curricula still happen nature yes it can really happened nature particles articles decay and the incoming particles of 1 momentum indicating the particles of other and that but is enough momentum was considerable assuming he 1 that it was so the incoming particle is described by of course is described by a particle coming outgoing particles Katie gone particles OK prime 1 K primed to the opera which eats the initial particle but call that society follow X misrepresents the particle being absorbed the point X and 2 particles created also at point X that's a simple example took our entire Co it is eaten apologetics minutes but to particles are also at the same point for simplicity but can can't in any place to go place and that means we have to the greatest of all space but still we get these ideas have creation and annihilation operators as some annihilation later in here which can annihilate just work on this article that article that sound a minus K and has an eatery or Katie acts and plots forget these filmmakers we don't need that independence here that's the operator which each article over here and there these 2 private others which put back the particles over here and they give us some 8 class of K 1 time a glass of came to and then there isn't he miners ii OK you want plus Kato crime experts say Max are putting aside their mileage particles we calculate the matrix element of cultural really only thing of interest of leftover is function of position is and toad but the pollsters happened and . 6 but this insects is special place it could happen anywhere we integrated over X we get into acts I dealt the function of momentum conservation I saw that process can happen with translation and variants in space and conserve momentum a fact it didn't matter how particles of comedian going out this little demonstration here but it will be focusing more translation invariant or the idea that the process could happen anywhere as with equally with food as momentum conservation the idea but it can happen with equal probability that kind that's energy conservation there was another symmetry we talked about the other talked about a little bit woes 8 possible symmetry if we multiply society bike he really high times land there were just change the phase of side what will that do the probabilities temperature well against it will do nothing to them as long as the same number of sizes backers of the same number of sizes side bankers that saying thing as saying that the number of particles coming here is the same as the number of particles going out and symmetry with respect to changing the face of the wave function like that is multiplying it by an overall families and multiply complex country by the opposite phase and that's associated with certain conservation laws such as conservation of electric charge consolation of electric charge because as that is contained In symmetries of the type period fees would charge carrying fields charged fields
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field for electrons for example if they were fuels for electrons and this symmetry would be collect only if there was any electrons in the initial stages in the final state the question Waldman nature charges conserved so wrong nature charges consider is the same as the symmetry under changing the face of a wave function these are some examples of symmetries right but that was quickly view now want to move on to the notion of a day later all Yap that would be good comes of age of all 3 components of the moment that didn't have a father you they are all for 1 Fall this never here some relative probability for different ways at the momentum a shared you have not had enough but not for not for this case he case basically neutral with respect to the ways of momentum a share you just did welcome back these things on the kind of welcome back toward will comeback I simply wanted to but some of those simple illustrations of the connection between symmetries and conservation laws and how quantum fields are used to describe physical processes to user creation and annihilation upon of particles now it is based on a violation operators what state at and I wrote that we should have brought is rated 1 of the of most is highly placed on the case 1 and I'll ask whether that means that if it did her job last a place of their their own Ms. Bhutto 0 0 it is now over right 0 electors oooh products distillates on the pilot from borders on the characteristic of both is 1st of all you cannot any number of them in any quantum state has described the couple matches ago they have a tendency to want to accumulate in the same stadium example Of that is if a particle decays and produces a photon for example and that the Kazan produces a photon it may produce a photon in any direction with any momentum are with on moved some probability distribution but if at the same time as it decays that happens to be on a large number of at times all in the same state of more of the same day with the same energy in the same frequency preferentially became so that time comes out has sustained momentum as extra photons which already there that's these square roots of it Our who does cut those operators fairyland on a different guns don't like each other like the country interesting state in fact they simply can't be in the same state is of course what those a discovery was 1st made by Carly ideas was probably probably exclusion principle and God in the context of Adams that 2 electrons never occupied the same quantum state with them and was generalized by Powell himself probably fairy others principle that fully Finland's of particles it simply can never be the same quantum state in Adams out of Adams viewers the a difference the bows out OK let's worked out some of the mathematics of some of the bill keeping the mathematics of creation annihilation operas is really a former bookkeeping useful bookkeeping but let's try the worked out a theory of quantum fields of riyadh particles Aken never be in the same state are we start with the same kind of construction as we did Phobos I imagine quantum field sigh of acts which is again exactly the same those of all our summation over all of allowed where does a court case usually all of the carried allowed a continuous because the will and not has operator for particle momentum Katie he thoroughly I K X states of the sister argue and laid low by how many particles each quantum state that the writer is never more than 1 state of the system is a bunch of zeros and ones no more than 1 particle state that's a chemical now or other kinds of things they can have 3 particles in the same state but not more offer must have more than 7 particles in the same state or other on varieties this is not our to prove that the mathematics of quantum mechanics together with special relativity dictate the only possibilities premier arms embargoes arms would pick us far beyond the class so that I could do that but we got going to describe the film honors at this it was exactly the same as formula is exactly the same as both runs side that same thing incidentally is long nonrelativistic particles will not get relativistic particles eventually but what the creation the same thing with the creation operators a eatery IKX but there was no different than before yet it a minus sign but somewhere let's focus just on was possible momentum the electric this could be electron was focused on 1 Parliament on possible state knowledge about all states publishers say say some particular quantum state it is the 1st of what China and they those of it only talk possibilities but represent that I guess we could represent a 0 that represents normal electron In that state all but 1 that represents 1 hour charter state this is multiplying is just to possible states but calmer here what is it out of the broad view of the abstract mathematics of the creation of militia robbery exceed what will sit with him make some guesses but we will make a guess creation from a state would not particle board yes want article or could they what about 80 creation operate on the state with 1 particle 0 0 9 0 0 does not mean the state would not particles it just means the 0 vector I don't like that Zook doesn't mean anything or just servers not director he's not state these were set up brother you have only operators on
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mechanics all operators a linear up all our mistakes about operators especially in quantum mechanics only Sonia operator I think that the medical terminology is operating usually means always means Lanier operator otherwise its operations with a much yes include mechanics operators are always Lanier operators OK let's see if we we can make some guesses What about a miners on all take that which is not there for Raleigh minors on the state was 1 particle but particles that network I these operators which we don't they do that is part of of the deal would dead as it is on muon example if we describe harmonic oscillators by way function ordinary wave then there would be a wave function for the groundstate nor a function for the groundstate discussed the wave function for the state would be Gao seen wave function like a minus 6 square that would be the way this would be identified as the Greeno state and therefore the state with no expectation in the wave functions sigh of X which is rarely equal to 0 0 at the Stade 0 Norway functioning or probability is just as you are from its not a state it's just Buffett that's this is a starting point for the algebra of fermionic creation and annihilation operators this year they know about our yes I suppose we should yeah you and it's a good point we should probably use different leather Carter let's not call for fermionic operators we could call alpha sometimes you sometimes seen as you want used OK the problem is that there are many in many different not inconsistent with many different no notations in the literature I guess for us we probably a wise work to use notation where bows make and fermionic operators have different letters resource so what's called this is a common notation also have a thermionic operators are labeled but they are analog preferred beyond eighties bows out lips but Sealy and figure out how what see daggers see you received last time C minus tires that operated do acts on anything but so let's figure out but that's what happens when on all well seamless 1 that's not just and see if the house is the disease not be helpful in getting it back to being on 0 0 0 0 0 this 0 you simply can't take away now there is a trial could not get the words you can take it away what about C minus on for that year C plus 100 goes on get what and then see my guests at his vote but could withstand was always as opposed to 0 so this is not the state knows it is exactly the same state which back exactly the same state what about steep losses seen miners plus steam miners See parts that addicts on Aug although of course it was a good 1 but some 0 which is a most to equations which is good for the Rams right so buyers the vacuum but let's Naoto the same thing acting on what was minus C plus acting on 1 while a similar system acts on 1 takes a particle lady and we use all the vacuum and C plus back right so this gives 1 back again I was a kid were acts on what standards this was a legacy of that's collectors and yacht OK now what happens for we do best that all because we can't is part of the Cold War utility present of its Vodafone Reardon loses oooh what happens if we're these if we did these 2 equations refined begins Class C minus a posse minor class on 1 gives more like both of these operators YBasub operator yes particular combination will acts on any state gives back exactly the same state so that's really and operating on stations by saying see past C minus 4 C minus past is equal to the unit operator His back the same state whatever backside this combination lot times mother plus the interchange call frozen minus here you go the kind here with a posse it's called me inside commutator was called as so far it is curly bracket sometimes curly bracket could bracket of AT&T is by definition a need possibly a so the 1st thing we learned is the creation and annihilation operators is that commute to give 1 right here this is incidentally analog phones yet as a matter which already like them our sins of the same but not because of majority like them in C policy legacy Siemens across the city has a lot of about on of a commentator on a minus with any plus is a global 1 CNO want the same thing stand or in this case it's kind of data about resigned in this case and I can't now about me and I can't get a love seat class with past you can't buy commutate ROC past received pluses just policy blast proceed past steep losses business twice simpler squared was is Guillemette on anything well and acts on the vacuum making created article but then the next 1 is create particle on top of a particle which is already dead he kid do that it acts on a particle which is then to that sort on
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secrecy plants always give 0 0 Price of Seat brass gives you are 1 of us he might seem like an iconic Paterson minus C minus at just twice C minus squared if the acts on a state with a particle before removes a particle and the 2nd 1 looks for a particle can find 1 0 yeah items they were out radical new 0 misses the analog from monarch oscillators on Conti patents down 0 0 0 shot this is an operator's now vector a CR polluters I operate a 0 . 8 0 0 0 such that when acts on any vector of any state it gives you a real will leave 0 exodus doesn't do anything to 0 is an operetta which is you know and as a vector which is 0 vector but a state vector state sector which is 0 2 different uses of 0 all but above 0 and back 1 0 operator acts on vectors state sector it gives the state equal to 0 0 OK but In those islands on apparel in mathematics to reach other where were obviously complicated but on your
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replaced by impact commutator from Iran and that as a consequence of this but you can't put 2 particles in the same state you you try trying to put C plus passed on all received last time C plus 0 as workers state with the equations says CPSC it was trip losses equal to 0 so all this algebra In cooperates and encompasses the idea but you cannot put 2 particles the same state described by these creation and annihilation operators I want to our observation about bears this easier crusade and annihilate particles we are given momentum what wave of what we assumed that some combination of proven assumed full from from these impact all incidentally yet is more completely supposing talking about creation annihilation operators different format KEK pride that I will just tell you this is Dr. KEK prying other words it's 1 FK equals Kate prime 0 otherwise in these in these things will issue 0 see missing miners but I just equal to 0 for a case crime that's algebra of creation a annihilation operators which if you like by definition the finds the algebra of creation and annihilation operators and the fact that
59:49
really does describe the only answer nature of course is marvelous correspondence between mathematics simple mathematics and physics but it interesting question as defined all this is that you can put 2 particles into the same momentum state you cannot make 2 particles carrying the same moment Delphinia told them eons of the same kind of currently cofounder of the same species you cannot put them in the same state momentum state can you put them in the same position state we will it With this thousands that if we find a particle that momentum Katie family on electronic we cannot find another 1 with exactly the same quantum state same momentum for about the same position could find particles at the same place you may not remember the but imposition of with the find out how they create a of at point X we could particle appoint X using sigh of xxx Silex former vacuumed represent of particles at that point acts he felt sorry I think we should so I'd better not creation offers so the question is what happens if you try to create look at the same point while we that means we're going to have a strong will also carry a hour seed class of class of Cape kind and then but still a let's do it theology which is good at position 0 than AIK Exs aren't ah 0 well was a very notices 2 all the others Europe aided the busier and busier any case you could like this In the 3rd column C cost of Casey Pocekay prime 1 half C Pocekay plus onehalf C plus of Kate prime seat plus of cake because it's summation here but this is just a hint that kind of 2 steep losses and that connotative steeper losses all equal to 0 so this is but what is are 0 if food should added that before because of backward yet but not right or is clear talking about only 1 Katie right it gets some little impact nontrivial impact when we generalize it in this fashion he took all Katie and keep Prime of those basically some physics that's going in here physics it's the physics that not only can you put 2 particles into the same momentum state but you can't put them interesting positions state for example on showing you is that with this algebra it 1st algebra is correct then is not just that you can't put 2 particles in the same momentum state you can't put them in the same positions infected can't put them in the same state altogether after but this was just an example of this algebra it says that you can not particles are sharing the same moment state or the same positions state or any other state matter is a fully on this is the the head of the house this is made it he did like a single with a lot about the current state can have 2 electrons in the same state now what constitutes a state constant state may not just be its momentum may be its momentum and it's been our which we haven't come 3 of the suicide of things that come to shortly is a concept the spin of important concept when can't do it yet so at this stage will imagining that a particle is characterized by a momentum of its affiliate beyond you can't have 2 in the same moment Kodak statement as of course you can't have them in the same state and of the state requires other ingredients besides momentum for example spooned them you can't have 2 particles of the same momentum until can elect like it way they have they passed that more but with no matter what movement Your canceling the higher dish electron maybe electrons and I didn't have or not momentum states there union atomic energy levels now the atomic energy levels over here and only here for 2 different Adams quite different way functions so if you have Adam over here and electron my occupy a wave function that looks something like this another animal he might have an electron which looks like this this would function that way functional the saying the quite distinguishable there by the fact that 1 of Leahy he alarms obviously yes you can have 2 electrons in 2 different Avon's both for example in the ground state threatening some particular state yet but you can't have 2 electrons in the scene that would require we are told that want to talk about an hour there a statement would be alright the right nomenclature is you can't have 2 electrons in the same quantum state in quantum state assist them means a collection of degrees of freedom but it doesn't
1:06:59
imply a particular state tonal ecchymosis system an electron can be easily any particular state nomenclature electrons system the state of the electron perhaps in particular orbital state Bruins and state me and they have a really good things like that To those narrow a likeness of packet here in the factory here federal here and now In the same state show them they're not the same momentum the same position right in call in big contrast the idea photon at times marched on the axis all for example in the same plane wave right as well you can't build up a coherent being of electron and that you can have a coherent Beamer of her you just can't promote so a family has in many respects a bigger abstract will at the same place no no no room you are you I had described named by a position or moment this is Our intertwine mutual had ever because a commutes with momentum and position but position and momentum commute so you can't speak about an electron at a position with a moment but you can speak about an electron a position with the particulars sunset that look like set out like therefore that since the disease was off not position Eigen states because the assumption was that concentrated but they approximately are approximately located the pollution of the out you can't put show them into the same and the same way but you could have 2 different which like cattle electron over here and the electron all but that the state is he a fire me I would have to refer you either to my own lectures are a book on quantum mechanics but just means it's the quantum mechanical analog of the configuration of the system the configuration of the system a system as a collection degrees of freedom and the Clarkson Nixon moment and things like that a state is a particular value in classical mechanics of the positions a moment in quantum mechanics estate of an electron is we everything you have to specify about the electron the state all the things a commune measured about electron all it's a wave function cabletron curator a about half obviously not 1 of them COM 1 of them's Indama galaxy but who did that the same commitment was above water Nevada and 1 Connecticut committee in the same state I can say that they say that they will be going to know where they are endangered don't really know their movement them with infinite precision so you know anything about where they are means that you don't completely nor the moment but yes end the extend that the electron and Nevada could have up pretty well defined moment but still not so well defined might mean Connecticut the fighting but not so well defined there might be Connecticut then yes you're gonna electron Nevada electron Connecticut which have a pretty much the same momentum but if you really tried to make their momentum infinitely struck actually Nevada would be equally likely to be in the Connecticut knowing Connecticut would be equally likely be Nevada and you simply can't disclose a deserted us get a but they soon will property be known it was far less we use the algebra of these operators in a very similar way we write down expressions involving electron operators which Niall electrons which take electrons out of the initial state creation operators which put electrons into the final state we can even multiply them by by armed by operators for photons photons incidentally being Goebbels islands now I can write mathematical expressions of EU process of some number of electrons comedian some number of electrons going out plus a bunch of photons and Wickham rights on what kinds of Rome bookkeeping as we used the described just a simple processes involving both are like a good bet now units this is the story of particle physics I you describe those reactions but before we get to that a couple more about the differences between their guns balls but got they got the ball back the believe worth it and on the US plant they are all but if there if there is the what is known the been The Barber of the was no the beans Connecticut the new not there yet the
1:14:11
flight path will get a let's imagine that Nevada is a point and Connecticut as a point instead of a big stake you appoint his Nevada off and he was the electron located right at the center of our I In Nevada not for neutron them for anything else not as what's political capital incidentally it is not an integer just Nevada and chanting Connecticut I'll call now the quantum state of an electron which is a superposition of being in Nevada and Connecticut has some probability of being in Nevada and some probability being Connecticut Nevada plus Connecticut This is not drawn with equal probability you should call the square root of make the probability Comerica 1 this a state of electrons which has equal probability of being in Nevada or Connecticut quantum states and if you look at a lecture newly defined in the center of the law or the sin of Connecticut with an equal probability incidentally another state like this which is orthogonal tour which was a minus sign here Her pay what you can't have used show electrons both in this on state you could have 1 or 2 Nevada 1 or turned in Connecticut but you can't have 2 electrons which are of both being equally shared between the Nevada Connecticut that has implications that probably not at all obvious to workers implications are but supposing we try to make electrons in this state you can't do it you can't have to elect charms Witcher equally shared 1 yes yes when Canada plus I'm me about my ships 1 electron could be in the state with a plot summary of the 1 by the time I was part of the Leo argued that facial saturated by 40 life if they not only a vital matter of days not number would in nonrelativistic physics there was no limitations of the speed of light In making the experiment forth at the same time means somebody condemn from here there were no time for that all this is not a figure that there was an additional fuzziness because a relativity about how articles are located but for the moment I want to deal with the number relativistic ideas let's let's calm movie grams state of a system of those on the ground state of the system of an electoral electrons to see how different they are but a the threedimensional world and since I can never draw 3 dimensions are only draw tools that ends arm I want to play off or possible a lot of men told eventual momentum misses the x component the momentum this is why component that really want 3 dimensions but as a civic and part of electrons electrons confined to be in a certain finite volume the final volume is very much like when we study onedimensional we studied electrons on interval of late with periodic boundary conditions but that's that's all here if electrodes are
1:18:57
confined the particles are confined To be within a given volume to the more than the art discreet remember the electron was moving on the chaotic interval it had moment Our which had to be what was there In now where an already owns to pioneer Tupaia Noel is able to Katie right so woes say we said if we draw the momentum access the possible values of moment the with discreet as well as a consequence on this basis fighting nite space available to the particle finite the lose the closer these levels get up let's continue to think about things confining the finite volume in that case wealthy X and light and Z components of a momentum would again be discreet so the allowable values of the momentum vector former ladders but not space momentum space the values of a possible momentum vectors but put 0 over here and there and then they go on forever not that it's not bounded describes on forever so said axis goes on forever Incan be anything so these other possible allowable values Of the momentum of particle in a purely patriotic threedimensional box let's start with bells on let's take a collection of arms or identical to each other the role the same kind of particle and let's put them into a box and must look for the ground state the state of lowest energy but after the 1st goes on what the got the supposed to go the lowest energy John Iwata 0 momentum the momentum put the bows on and that's 0 KXK why is equal to 0 at that point that the singleparticle state our lowest energy energy is case square with 2 M the latest possible energy for that goes on Mr. carries euro momentum if we want to find the groundstate state we just put in the particle was 0 momentum now supposedly 1 and other particles to that on the same kind with good but to keep a theology as long as possible set in place now at the same place Rippetoe particles in the same place and fact would put all in particles and place that'll be the state of lawless energy source that is called a buzzer condensate that's roughly on the idea of a a condensate is a large number of particles all in the same state or in this case all in lot energy state available incidentally the lowest energy state available since it has the lowest momentum shoppers and function which fills up the box is function which fills up the box and so they function each 1 of these particles fills up the box and simply put up articles in all of them uncertain about where they are in the box for a lot of bats 1st local buzzer condensate and source of the ground state of the system of HBO's arms deal a large number of particles builds up a kind of classical field strength so that the shredding the wave functions pretty classical OK it's very very different know what happened if we had unit from Iran's forget spoon Mecham interested Spain now where we will eventually would put the first one of the Kowloon 1 at a time when I keep P & G's law was possible and obviously the first one the call in with 1 foot in the lawless state what about the next 1 whatever the next energy level is already here the next 1 would maybe go away he said that happened before states of the same energy so we could put here here here here this in 2 dimensions and 3 dimensions there would be no luck and success 6 states altogether so but can't put in electrons there will fill not be states now but and the electrons we can't put them in the same state fourbedroom so that's probably in the next lowest energy level which will be over here incidentally the energy being proportional case squared is proportional to distance square from theology so we to keep theology low as little as possible is cloudy electrons in momentum space as feeder as we can never we have a lot of electrons would put me and they will fill up in momentum space focus Phillips a sphere it might be a little confusion about about the jaggedness of EU spherical but that's this have a lot more energy than the corresponding bars on system the corresponding on system had all the particles in the lowest energy but you look particle while you will find is a particle our 0 momentum and the grants the of mini firmly on system you will find the meals you put in the higher the maximum that momentum will be there will be lots and lots and lots of particles of large momentum because only a handful of because there aren't that many states at low momentum clearly more states within a given shelter large momentum personally energy of the system will be much higher good things guns into idea 280 box costs more energy warned No. 2 losers pattern that they feel a lot a years out some boundary with boundary is determined by how many electron to have depending on the number of electrons ill photosphere atmosphere is called the Fermi sphere called fairly sphere the history of this will be confuse it with the Racal figure out for me arms and that's where the coffin as Einstein a figure bonds ions in that time Yukon Ellis Island no jail contributed heavily to the subject anyway this is the groundstate part of a collection of fairy arms the Fermi sphere Webster over here because I think momentum space momentum space at drugs
1:27:06
lines died just all particles condemned the end of the year momentum space for HBO's was mere let's the slightest so we can see you're with the next states are what's the 1st what's the 1st excited state we have is but on all the center what's the 1st energy level above the ground state what's easy we take 1 on and move it the next energy level we take out windows on the ground state and put it into the 1st excited state which would which bars on the windows the matter saying so we have in mind this 1 bows on in the ground state and 1 goes on in the 1st excited state for 1st excited states that port the 2nd excited state in my car spun depending on the details of my correspond putting 1 electron 2nd excited state of tool icons and the 1st excited state but 1 like 1 excited by electron bows on a variety of different things but you could see the way they have to excite the system to give among energy is to take electrons from the ground state and put them in the higher energy state let's come to the Fermi system will also very similar but let's try to figure out exactly what would correspond to the lawyers question of lowcost plant may not be exact lowest energy state but the very lowenergy states above the ground state wheelerdealer just a little bit of energy what's the cheapest way to give energy should we take electron from the center here and outside the can't know when electron some someplace inside a Fermi sphere because electron I think as you were about the say it would be too smart taekwondo deep inside the Fermi sphere and bring to outside because that would take a lot of energy it takes how much energy you could walk out of low energy and put back a relatively high energy that's pretty costly what's the cheapest thing right taekwondo from near the surface of the inside the theater and with outside how much energy that costs not much because you've taken a pretty high energy electron just displays that a little bit in energy and saw that creates an electron out here with a little bit of energy above the edge of the firm but also leaves something it leaves a hole in the from ECU behind it that plan is saying Let's opposes a really electrons a committed but consider a realworld situations we have a box and that boxes full of all the positive charge positive charges protons of course or nuclei but simplicity let's just imagine the positive charges knew over the box and they would put electrons and on top of it and put enough electrons in Philip families feel like that's it typically neutral because are many electrons is are protons and a box of electrically neutral in the ground state the family owns 4 up from reserve this very sphere here now would take an electron out from just below the Fermi sphere and put it in just above the atmosphere will not change the charge it still electrically neutral but we have created 1 extra particle a little bit of extra energy above the Fermi surface and left a hole in the Fermi surface and a or were missing particles I'm missing particle think of it literally as a whole it's an absence of a bit of negative charge the negative charge with a certain momentum over here because we thought of as the president's I a positive charge hold off welcome to the as a kind of particles in this context or behaves as a particle is a particle of negative energy because below the from now let's let's see how much energy it takes How much energy does it take to move a particle from here to here well elsewhere let's just say we talk out a particle Our energy that's called particles but we took out with call energy epsilon now we put in another particle of energy epsilon Prime we took out the particle of moment of energy at a much energy costs some book so either the I'm son perhaps but now that now that you have site of the new millenium more precise but it is different but the for that redundant I'm getting tired reaching a point of fake the poet is a cost of energy because energy up play brigadier obscenity and this is what I end what oppose U.S. how much energy after putting you have to put in and be an amount of energy that it would take to remove this particle and bring it exactly to the Fermi surface and an additional amount of energy to bring it from the Fermi surface Air off firmly surface artery is a picture arm it is a fairly the firmly surfaces EA due for release let's take a particle just below the Fermi surface bring it from here to here How much energy does it take what takes time bits of positive energy we can temperatures were the 1st 3rd of positive energy is the the energy that it would take to remove this particle and bring it right for the Fermi surface but so will the positive energy to bring here and the wound up positive energy to bring it here was that the sum of 2 positive heard the deposit terms being the absolute value of the difference of the energies from the Fermi surface if they had too little bits of energy none of that can be thought of as the energy of the electron over here measured relatives of Fermi surface and the other 1 can be thought of as the energy of the whole above positive this 1 has been a positive charge because of electron this 1 has a bit of negative charge because missing not but it this a bit of negative charge because of positron now that the purpose but added
1:34:59
that the negative charge innocent of Chun and this owners of the depositor Judge Rico it's very well thank you right now there's electron could be moving and then suddenly pop into that hold the is available now the home is available for the electron to drop them into a just as an electron dropped from the excited level an Adam down and on the occupied quantum status is occupied quantum state this electron could drop down into this hotel whatever happened electron drops its energy and showed into the hole that energy has to be conserved so the energy of the electrons decreased photons emitted per say another Neukom say an electrode comes together with the hall and annihilate electron violates the home and a photo or more fell apart on more than 1 4 times the number price goes up thinking speak about this in the language a hotel is a kind of particle Gaza to fake particle with some real particle intern real sense of the word but could take particle it has the opposite charge of which will electron accountants have some positive energy and wind the electron drops them for the whole you could think of it as electron coming together annihilating and producing some heat radiation whatever the processor annihilation photo yet they were last ladders lament the spades yup no not now moving from 1 energy level to so if stay an analog of having an Adam but let's speaker but him order with the means of atomic physics atomic physics the box could be did not momentum space box with a box confined electrons could be added to leader the that time of the center some positive charge and we fill up with some negative charge Our electrons progress in this case the proton charges not smeared over the Adam so it's concentrated center it's a little bit different but we take an which has the same number of electrons and photons we start with all electrons in the lowest available states lowest available space programs stateofthe Adam are vastly analog of filling up the Fermi sphere here now what time comes along and had an electron and pick it up until an excited state at that time comes along and had an electron just below the Fermi surface and picks up above refers that's a lowenergy electron along with you twophoton so it doesn't have much energy it can't take electron from the center here and made it to the outside political lot of summer a lowenergy photons and comes in an orderly can do is hit an electron will be absorbed by electron near the Fermi surface and kick it just above the Fermi surface another language it is a time has annihilated and been replaced by a particle or electron alcohol so it's particle hold creation by taking me energy from a folk on the same way the photon Madam excites Adams of course when excite C Adams it leaves a vacancy vacancy in this language is called a half hour also has some of the 1st full year of gave him a list of nearly all the lowenergy photons website 80 hours of radio waves of time energy and try to to get absorbed by an electron near the center it just can't give that electron enough energy to get out of the Fermi sphere it can't jump to any place inside the firm is for you because a reoccupied enters a low energy photon can be absorbed by electoral process was is located welcomes for a high energy photon of course that can chicken electrons from deep inside the school language is that things inside the Fermi sphere are in the see SEAT is deep in the funny seeing this is near the surface of the Fermi sitting on a high energy photon or collection of highenergy photons coming together can kick an electron from deep inside the Fermi outside a lowenergy photons could take a shower electrons forward just beneath the surface area just about young that nothing except Nora near not on interactions between electrons make a study somewhat more complicated but interactions between electrons are pretty weak pretty weak and very strong and for the most part the Arabic be ignored by metal the boat I have had enough but that is not what get out all if not yet about what happened today said if it does 1 electron get excited in back but anything can happen as long as it consist of conservation laws think about our but at a much lower probability process to create 2 electrons and pool halls they take that to electrons it would make so that would be a process in which particles were full of articles were cradle together and that's as much as likely I want the opportunity Metro took more likely but if thank Is there these photons simultaneously yard that or what I would do it over there to more the review which is the problem what is left of the fuel loaded beat but that not that the overall it doesn't take it just accept kind of energy work to kick it from year
1:42:45
to year Seoul yogurt energy which is so long as but yet I have but now best if Paul everywhere were due for Carl for later use stock collection where Washington death he there will be blood but it Dad or if they had will pace classes as well optional resilient said that there's a lot he now but there also also in a back room sea of positive charges I sold the whole thing is electrically neutral lecture on interacting with each other the electron interactions pretty weak partly the week because the electoral charges screened by about the year proton charges but I really didn't want to get into the electron interaction that that's a separate issue were over I thought that screen the just talk about among young Manitoba but no screening is important phenomenon in particle physics and has a catalog here but let's come back to well I forget to was the Dirac equation 15 minutes to give you they're very varies simplest version of the Dirac equation which we come back 2 repeatedly but very very simplest version of the Dirac equation was sort of complete a story here United's William Styron parent company study by the impact particles holes ntype articles but what this is what does this have to do with not a metal in a box but with the relativistic quantum field theory in the vacuum of particles and by particles so spend just a couple of minutes giving you a very very simple as version of Iraq's logic and to keep it really simple let's stay with onedimensional space onedimensional based on only 1 of them text will combat a modem and next time then let's ride a wave equation this wave equation as beef from field where costs high off fright this electron is known electron neutrino privileges it's a particle it's Tiffany on From but happens to move the speed of light because of the speed of light and that means or maybe a equals came right equals Katie is the relationship between frequency and wave number or between energy and momentum to 1 maybe Kerry another possibility for made physical to carry their your possibility you might escape OK but let's take all mitigate equals what kind of wave equation doesn't correspond to well that correspond to the way the equation aside by DTE is equal I think it's minus b side by DX this partial murder this is even simpler the following a equations that while I say that this is purposes only equals case but legend society is equal to eat I K X minus Omega besides I D T brings them a factor of my ears Meyer may decided by IDX brings a factor lf the the relation between Omega case is just all make equals corresponding to sequels 1 then that just decided by deep musical minds to starboard like I said this is a very very simple wave equation that describes a which only move in 1 direction we cannot move in both directions moved only as it for the life New coast but yup this in these waves move right will it take to make waves a motor left we want to be sad IDT Eagles plus cyber IPX with either of those equations you of particles which move in 1 direction but in this case of right and suppose affiliate and for certain with imagine they carry electric charge of electrically charged that OK now something a little bit crazy about this whole Maggie equals K energy equals momentum Kim KB negative showed item right like right equally IKX Beckham also writing of a minor sigh kayaks Icahn like both possibilities things which the 4 but there's something oddly enough probably a little bit dangerous about negative values of k carry negative values may again a negative as mean what negative energy so this seek describes a lecture chance of positive at and negative energy which drew a picture making equals case a leg equals carry may go vs. case the shellfish headline the K cars on the energy is positive for negative the energy is negative
1:50:34
quite simply described electrons which can have either positive or negative energy our that sounds like trouble wiser trouble White electrons with negative energy trouble wealth of electrons have arbitrarily low momentum remember what happens in Adam while to an electron which is excited it really gates and drops down to lower state if the world unbounded lead low energies arbitrarily negative then electrons but say positive energy electrons could be photons and drop them energy but that would necessarily have to stop at 0 energy they could keep dropping down dropping them dropping down and make arbitrarily negatively energy electrons while at the same time pumping up the energy of electromagnetic field is very dangerous and is something wrong or you can't have all arbitrarily low lowenergy well what is the lowest energy state of the multi electrons as often as they get a lot of memories here in this case the that issue in in this case is stocked with support we have a zillion electrons earnings we like and we put the 1st electoral system would because interloper steadystate because the state is when Alabama may have some wears off minus infinity somewhere the next 1 of amongst this is a dangerous is a bad idea what not said that this is a simple version of Dirac equation This is a Dirac equation 1 the match with Barak said is left pretend that all of the negative energy states were filled just like filling the Fermi sphere all the negative energy states what up Kazuo energy sold all of these states of the old with electron every negative energy states you can't make a state of low energy than that incident at the lowest possible energy you have you fill up all the negative energy states every time you put a negative energy thing in that lowers the energy put many negative energy states in his you can now start putting in positive energy electrons that will increase the energy of the very lowest energy state before you could call the ground state is the further with as many negative energy electrons as there are negative energy states and that starting point starting point would not electrons you starting point is for what completely the negative energy state that's the vacuum that space according to Barak's theory Barak's simple version stop that since a state of lowest energy let's call it a vacuum and that can lead do you couldn't take the only thing you can do do is take an electron out of the city negative energy C and the positive energy electron from over here and put someplace else what properties of the state with 1 electron all he ever with positive energy and positive momentum and 1 missing electron over here it's a this intellectual what I want to the you at it well remote executive yes normal the lecture part of negative for positive a positive positive wiser positive news missing deficit of negative momentum I'm so it does create a positive energy positive energy electron end a positive and positive momentum created to positive momentum objects are both moving to write our 1 with plus charged with my discharge electrode this charge and the missing a lecture having positive charge negative charge and positive church that that in summary and who would do this more completely but that was direct theory of electron the positron of positron was simply all in the infinite negative energy you want them this equation of a generalization of look bad and so I love that equation that goddess terrible disease of having negative energy states not problem is a you can't put more than 1 electron in a negative energy state so just completely and back empty space recall that empty space what you do to you could remove 1 of the negative energy electrons and put it back as a positive energy lecture but back yes but backers positive energy lecturer and that leaves a hole and back said that Hollywood is a particle of positive the charge right now at 1st he was excited because he goes wasn't far from easy to prove that they met b a particle here must be the same as the romance of the particle and hint that particle purse was discovered a particles articles but this was a basic logic was equations like this which led to to it most were the last to be and you try to describe a bottles on this equation that would be a madhouse we'll just keep putting particles into the negative energy lost as many as you like and there would be no ground state programs they give just keep putting in more and more than 1 negative energy bows on so this way thought this be equation only makes sense for affirmed its would not make sense for both on and where that was next good discovery that from Iran's can be described by a Dirac equations like this that would not make sense for both arms why does the reasons explained and the idea of entire articles on who will come accompany end that particles from those next time and will discuss the Dirac equation and more costly the real Dirac equation This is a key element you version of it yeah who can't or expand the number things along with this electron for 1 thing almost right that's crazy for another thing it's got it it most of the speed of light that's crazy was a number of things along with its electron Buckner the but neutrino what's neutrino the neutrinos of goes on the neutrino was a bows on the opposite the neutrino that's not quite a neutrino because of the tree also has for more please
1:58:22
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55:56
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Computeranimation
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Fahrzeugsitz
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Optische Kohärenz
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Metadaten
Formale Metadaten
Titel  New Revolutions in Particle Physics: Basic Concepts  Lecture 5 
Serientitel  Lecture Collection  Particle Physics: Basic Concepts 
Teil  5 
Anzahl der Teile  10 
Autor 
Susskind, Leonard

Lizenz 
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DOI  10.5446/15070 
Herausgeber  Stanford University 
Erscheinungsjahr  2010 
Sprache  Englisch 
Produktionsjahr  2009 
Inhaltliche Metadaten
Fachgebiet  Physik 
Abstract  (November 2, 2009) Leonard Susskind gives the fifth lecture of a threequarter sequence of courses that will explore the new revolutions in particle physics. In this lecture he continues on the subject of quantum field theory, more specifically, energy conservation, waves and fermions. 