Supersymmetry & Grand Unification: Lecture 3

Video in TIB AV-Portal: Supersymmetry & Grand Unification: Lecture 3


Formal Metadata

Supersymmetry & Grand Unification: Lecture 3
Title of Series
Part Number
Number of Parts
Susskind, Leonard
CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Stanford University
Release Date

Content Metadata

Subject Area
Ruler Weapon Girl (band) Prozessleittechnik Day Schubvektorsteuerung Short circuit Amplitude Summer (George Winston album) Global warming Cosmic distance ladder Particle Variable star Bird vocalization Separation process Roll forming Lecture/Conference Institut für Raumfahrtsysteme Steckverbinder Month Magnetic moment Divergence Vertical integration FACTS (newspaper) Belt (mechanical) Computer animation Particle physics Mass Maxwellsche Theorie June
Matrix (printing) Grey Bestrahlungsstärke Schubvektorsteuerung Amplitude Order and disorder (physics) Crystal structure Annihilation Cosmic distance ladder Watercraft Particle Separation process Lecture/Conference Boson Electric charge Rail transport operations Dolch Cylinder head Refractive index Electronic component Minute File (tool) Vakuumphysik Electronics White Pair production Excited state Spin (physics) Gedeckter Güterwagen Particle physics Cartridge (firearms) Signal (electrical engineering) Week
Ruler Cooling tower Effects unit Schubvektorsteuerung Scale (map) Year Summer (George Winston album) Interval (mathematics) Cosmic distance ladder Particle Roll forming Lecture/Conference Continuous track Tool Hose coupling Magnetic moment Water vapor Kontraktion Vise Power (physics) Flight Spant Density Belt (mechanical) Sizing Cartridge (firearms) Chain Mass Measurement Noise figure Ground (electricity)
Ruler Speed of light Short circuit Year Force SEED Cosmic distance ladder FACTS (newspaper) Particle Absolute dating Bird vocalization Roots-type supercharger Wavelength Belt (mechanical) Mass Compton scattering Magnetic moment
Matrix (printing) Prozessleittechnik Capital ship Scale (map) Amplitude Order and disorder (physics) Cosmic distance ladder Watercraft Bill of materials Particle Pattern (sewing) Tool Magnetic moment Speckle imaging Car tuning Videotape Refractive index Bracket clock Single (music) Power (physics) FACTS (newspaper) Belt (mechanical) Weight Autumn Chain Mass Jack (device) Food storage Gas turbine Measurement Switch Microwave Schubvektorsteuerung Supernova Crystal structure Mitsubishi A6M Zero Basis (linear algebra) Alcohol proof String theory Negation Gamma ray Leistungsanpassung Star Cylinder head Cut (gems) Doping (semiconductor) Electronic component Map Fuel Sizing Plant (control theory) Bow (ship) Miner
Theory of relativity Weapon Prozessleittechnik Hot working Transmission line Amplitude Order and disorder (physics) Foot (unit) Bill of materials Particle Separation process Fermion Automobile Tool Boson Rail profile Wind farm Hose coupling Moon Quark Magnetic moment Dolch Ballpoint pen Faraday cage FACTS (newspaper) Excited state Bow (ship) Mass Flugbahn
Hot working Scale (map) Printing press Interval (mathematics) Cosmic distance ladder Roll forming Band gap Spare part Stream bed Book cover Mining Hose coupling Progressive lens Divergence Sensor Combined cycle Ballpoint pen Crystal habit Electronic component Power (physics) Source (album) FACTS (newspaper) Pulp (paper) Cartridge (firearms) Bow (ship) Mass Measurement Noise figure Ground (electricity)
Computer animation
Laos Stecher University look
I I was I was going to start talking about supersymmetry today which I will be back I'm going to talk about supersymmetry today but I want to go back over the motivations and just read Keep some of the things I said I don't remember was last time I think it was about divergences in court and field theory in particular the divergences which have to do with the renormalization of the masses of particles and not sure I sit it well Amendola go back over it and discuss it ever will more lanes and then start talking about How supersymmetry repairs the damage of our summer days problems I honestly cannot remember where I everywhere so if I say the same thing all over again too bad if a for set reply evacuated an arm of Goss all particle physics almost all particle physics not not particle physics but a lot of particle physics is dependent on computations of fine diagrams and find in diagrams could stand or can govern a number of things they can 1st of all of Governor needing to save you use them to calculate scattering process particles Camille particles go out and you want to calculate the probability so that's 1 thing that find diagrams do very efficiently you have the sum up all finding diagrams accord for the calculation another thing the vitamin diagrams do is are they give you the precise words the precise words as they help you calculate be effective Lagrangian is an effective Lagrangian as opposed to it in a fact in an effective Lagrangian not all that stuff quite the right idea month speaks about effective Lagrangian was gone this is not a tiara a description of approval for for this particularly Grant Jr. a very effective not to ask what you mean is it and approximate were burned during approximation of the exact same with which is best set to add on removing lot of the complexity which was complicated to calculate the sector on June typically involves cut off another words a small as distant already a largest momentum and say something about finding diagrams and I haven't emphasized we did discuss proper hunger combative them in a moment but propagator is are if you like the amplitude were putting in a particle 1 place taking it out the place their functions are relative coordinate their functions of a thing that I think we called Delta member and ushered member but belt understands the difference of these 2 positions as delicate as a 4 vector of course so it has in the cities of the meal the propagator is a function Of the separation between points it can also be 408 transformed Baker before it transformed and expressed in terms of a function of 4 show other variables before it conjured variables when the call real name for the Fourier conjugates positions momentum right so the propagator can all and usually the finding the right of final rules Our expressed in terms of momentum but let them do that more complicated you have to worry about momentum conservation or what sort of things off but the other way to describe refinement diagrams in momentum space and in momentum space findings Bagram become integrals over momentum for example In a fine and Ira right best but Gore 1 let's take a simple 1 much support would only let's start would be very simplest by the diagram I can imagine Mr. close lope with no particles coming in and no particles going out that if you like can be thought of as a propagated connecting point with itself Aum we could set we describe it 2 ways we can describe it exactly that as a propagated going from 1 point of the same point or we can describe it as if the girl or some integral although all the moment that second-floor around inside disclose look we could think of this now are finding diagrams are always sun's over everything can happen so we can think of it as the particle going from 1 place to another that's 1 thing that can happen although it could think a different way we think of it as it particle going around this closed loop of momentum k ee and they the propagator has some form in terms of momentum space but the important thing is that the diagram becomes an integral Over momentum space and the global momenta area Alomar mentor their intermediate moment that there are very high moment but In the divergences that we're talking about can't I don't be thought of as In pity which occurred because the 2 points in this propagator are exactly the same point another words a short distance small distance there is a fact propagated becomes very large when to point to close together all we can think of it has divergences which happened because there's just told me much momentum space to integrate all over the Moors divergences which happened very very large momentum what's the connection between large momentum small distances well that connection is an old connection that we know about it's just a fact that momentum is related in inverse waiver Lange and large momentum is associated with very small wavering that's also we could he
described things in case space already X space has dealt that here is really about the exit difference of 2 Exs so we could describe the propagated in momentum in positions that all we describe the momentum space if you like sometime in the future of the review how find diagrams of described in terms of momentum space for tonight our visitor can remember we do this before possibly repeat but nevertheless for us it was a good 1 for 1 worth learning about the question is what it is propagator between 2 points various kinds of particles that basically there are 2 kinds of particles in Blachly 3 kinds of particles particle physics there are particles of spin 0 not too many of them only 1 early really comes up in the phenomenology of particle physics and it's their Higley we bars on the pigs bars on but said it does exist Albert it doesn't exist there we all over her troubled souls yes we do think there a scalar particles were kind of particle and the scalar particles was mean scalar particles means it's been 0 and 2nd of all the means that the field operator for it is a scalar only 1 component known multiple components and the propagated van which may write down what the expression for the propagator for a scalar field is not America expression above the quantity that were talking about you start by putting in and 1 point scoreless at 6 and with scoreless Hawaii and the kid XOY both for vectors and that is the difference between themselves to Ikot distant y minus X Delta is on ls based on space time and X and Y can be arbitrary point space time separated by distance Delta then the definition of the propagator it is to start with a vacuum you will create a particle at point XRD you do that you do it by applying the field operator at pouring you take me in a product of that with state that deal with exactly the same kind of thing where you create a particle at if I another words it's state its fee but amplitude that if you put in a particle next you will take out a particle or you will discover a particle at In a product between East things works right that then quantum mechanical in product file all so no 1 he could think of it as an amplitude for a signal to go from Nextel why if you like but also happens to be another thing it's that exceed expectations value of the product of the field 5 x 5 wide in the vacuum states us both of these things whatever it is it is it is a function of X minus white and it is feared that the thing that we call propagator OK now that's its definition are what is its value that depends of course here I'm writing down for scalar particle fight you do the same kind of thing if the particle is 8 fear spinner hats that's just right over here and the particle were firmly honest and a half minutes described by Dirac wave function of Dirac field outside sigh has some components now a May components does a fermionic field have 4 for complex components now over some vessels formula it can have all week To but let's not forget that right you could have separate left-handed and right-handed affirming on your which case is allowed to be too late to comport but that's not important hasn't components that also depends on position himself for firmly under orders from X Hawaii the corresponding thing would be the vacuum expectation value or risk the vacuum expectation value or the propagated from extra wide of it could be for example sigh dagger of X times sigh of why you put up parlor you put a particle next you take out why it also has some components and has some non-trivial index structure is that structure is indices of firmly on-field spinner indices the spin 1 through 4 not associated with component is based but components of vendors so whatever it is it's a function which depends on 2 positions and also to industry I Jake of course you could also study E-II component but there but in general it's a matrix and the IGA space and also a function of separation known suppressed Peter issue on these matrix structure brewers EIJ structural suppressive finesse just avoided and discussion a little bit complicated not terribly arms but for the being sold what 1 of the 4 of the Dirac before but for Dirac matrices since this is a matrix of 4 but for matrix it could be expanded in Dirac matrices if you like yeah I Kobe depends on it depends on whether these scalar particles charged the former head of the scalar particle does not have any charge you don't have to put the dagger the dagger the field is revealed in the field Israel consist of both creation and annihilation operators for the same kind of particles so for a neutral particle like Higgs boson on you wouldn't have to protect the electron for example electron discharge a difference between science that but this is not the
ego these are important thing at the moment now the question is what kind of functions Delta Is this propagator and that can be figured out just on well OK let's begin with massless particles for massless particles where there is not all are the scale of the problem no scale the problem of other than the distance between these 2 points That's the only link scale is may is inversely once we said H. bar equal 1 these equal to 1 a man is in inverse late so when you specify unmasked you're also specify the length scale but if we're talking about massless particles then there is no only scale in this problem other than the the distance between X and Y OK that's the only link scale the problem so dimensional analysis alone is pretty much enough to tell us the form of this of this quantity wants this demands for the friendly offer particle that is more complicated and can be completely guests by you have dimensional analysis but let's start with the mass case with massless case all they have to do is figure out what did they mention of sigh and sigh on and the way to do that is 1 basic rule the basic rule is be actions it is always dimensionless know what's the units of action normally fields of action from of action the effect of the same as the units of 8 bar but are equal the 1 means of actions of dimensionless so action the only cool the only things are interested in the length scale lengths or masses length times masses if C is equal but 1 that links and time have the same units Lincoln as saying units and they energy on momentum has units of In the 1st Lane that's the way you keep track of dimensions so let's figure out what the dimensions of flying apart we starlet action for 5 times so simple action the simple expression for the action of a scalar field with them as before and that will be for X and the growth of space and time of a Lagrangian density and the symbol of our city for a scalar field is for example just derivative of flight with respect 2 x mules squared with squared means year the appropriate of contraction With better consult for blood as far as units
skull it's just a river of fire with respect X before Thaksin and this is supposed to be dimensionless so let's calculate the dimensions of Friday Healy have for what powers of Lane and the powers of going downstairs found to cool the river fire with respect acts as a link downstairs so this whole thing as it would end EU it's a fire or whatever they are that's close units rapid-fire we haven't quite story Haverbrack square on the dimensional aware of 5 the violated by only squared provided by only kinds owing times alliance could link the some other 4 what divided by link squared times squares just by intentionally not keeping track of anything except the mentions this quantity as units of links square comes with dimension of fires square however actions are supposed to be meant of the actors dimension was the only conclusion is that of scalar field like fight as units of inverse Elaine right mention of fight is Enders late Vice the mention of 5 is a accord the 1 let's just check with a goal will be further forever AN another turned around Lagrangian let's end in mind this and squared or tool of friend master times by square and still dimensionally consistent fire still has dimensions of late summer minus 1 so far I squared is where about In what about a man now is like a momentum or energy and has units of In slain NASA's units of inverse laying just as momentum does so this has units it most Link squared just like the rivers of respect X give you an inversely quake squared another in Brusly square this is In the 1st lady of 4 times late so before so it still works out but still works out that man in other words the man's correctly has dimensions of inverse Lane we 1st used we can make Turner nor grungy Inc tell us what the dimensions of fine art and then we can go and check that the dimensions of mass offered dimensions of mass supposedly ended another term he puts a land fight before what would be the dimensions of land Jack fight as units of immersed lengths of for what inversely 0 4 times late 0 4 that's dimensionless so what has to be the dimensions of Lambda dimensionless right dimensionless so the 4th couplings constant is dimensionless carries no dimensions of makes a kind of special actually but and joined the fight over 6 himself what are you could best you could tell me what the dimensions are by the same kind of rule by let's suppose now that the mass of the field 0 EU which case there was no link scale and the problem others then belt then what must be the propagator fire fire wine and their Mitchell grounds it has to be in inverse links square 2 205 each 1 in restoring it can only depend on the distance between X and Y that's the uniformity of space translation and variants so it has to be translation invariant which means that only depends on explains why vestibularis invariant which should be the same if we rotated the Lorentz frames that means it can only depend on the proper distance between X wife and the lowers the proper size the proper ladies of the interval dealt nothing left for it to be next step 1 over the square where you just say what the square means got the square means Dr. Newell dealt meal another words the 4 vector interval between X and Y at all that's the only now when I see the only thing of course that could be a numerical constant and there is a numerical constant pieties floating around but and you can't get the pies from dimensional analysis you get pretty easily but not From the House's so apart from numerical numbers of water 1 things like Popeye immediate tool a for in theaters we our square Neligh happens when there's a mess mess when you when the semester
problem is the larger fund the propagator and as a general rule things a very very large momentum forget the fact that a particle might have met with me give you an example the energy of a particle momentum P the energy of a particle momentum P is the square root of p Square square SAN DIEGO particle where this after 1 of the speed of light in there I would stick us seed see square the seat of former but let's forget that musical The 1 What's the energy of a massless particle energy of a massless particle is just E is equal to the absolute value of Pete y happens to this expression when P gets very large P gets enormously large much much larger than it becomes a good approximation justice said it's the absolute value of pity song is an example of how will a particular formula forgets the fact a mass when the momentum gets very very large large momentum typically means very short disdain sure wavering so it's a general rule that things like propagator is all become insensitive to to the at very very small distant the dominated by very high momentum when you think about propagator on the Fourier transform of the propagator it's a function of momentum and very very high moment the value of that propagator it gets the fact was a mess but the high momentum value the propagator was intimately connected with a short distance behavior propagator so very short distances we expect that this is correct even if there is a man while the Delta squared is the way the propagated behaved even if there is a massive problem now 1 of is how is it correct its corrected by things which could be important at large distances but stressed draw a year 80 but Yiddish graft this function with Graf the function and blows up at small distances falls off but former Delta square smoothly against the particle has a Mets than the result is that the propagated 4 wars off when Delta becomes bigger In 1 and 1 of them in the Compton wavelength of the particle androsaemum when Delta gets a larger than any other than the inverse mess of particle the particle does have a harder time propagating from 1 point or another words master lighted propagate along way massive it can propagate so we long way that goes back to a reason why forces mediated by mess was particles a longer range than forces mediated by massive particles solve the typical kind of thing that happens approximately is not an exact date is that you get some sort of thing like each Delta times and which hits small we doubt that is bigger than 1 over and this is the kind of correction that comes from a mass going don't that is very small This is not very significant procedures warned with Delta is very small but when it went down as large this just cut off now really wanted to be precise it doesn't really quite look exactly like this war over doubt the square was not exactly 1 the square it's a little bit smaller than 1 Delta squared the fact it's a little bit smaller at every value of belt that so we really want applied carefully plot the massless and massive propagator would always find Mr. propagator was a little bit smaller a mess was propagated goes off smoothly and here the this of the massive propagate it would be a little bit smaller I it's hard for me to draw this but it would be a little bit smaller at all values of distance so that's 1 factor with that they would have the same asymptotic behavior had dealt equals 0 1 over the square the use of 1 will always be be a little bit smaller propagate would always be a little bit less potent service be OK so let's see was propagator sorry that's the young the scalar propagator end think we did talk about this now are beginning to recall we talked about a finding diagram with looks like this is the simplest diagrams you can draw it represents if you like 8 correction this could be a scalar particle would think about a scalar particle this is a correction this would be a correction coming from land the fight he is a vertex involving 4
particles tho it didn't allow 1
2 3 4 and this would have weight land times the propagator From 1 point back SINGAPORE now this is actually a correction of a mess terms of the scalar field E M Square I Square D M Square fi squared represents a diagram were particle comes in and roars back out absorb 1 Henry admitted in aid has AT coefficient are a string and square foreign Square to report this is a collection that it corrects these amplitude for particle to come in and see and just go back out from a point how big is that correction is is given by the finding diagram and the Final Environmental Lander times the propagator for dealt the equals 0 so the answer is crazy the answer for this process here is Delta divided by square miles of land provided by 0 squared or Delta square Tiffany Is that its infinite that we can't trust our theories of arbitrarily small distances presumably we expect that there's some kind of fuzziness and nature are very small but as we know very little about gravity my created something else beyond what we actually know might create a degree of fuzziness and if the fuzziness it is on a scale that scored small Delta a big dope always bigger and small white small Delta is the smallest possible distances of our own imagination fairy likely the plant scale or maybe some unification scale very likely a very large energy scale maps are a very large momentum scale small distance scale then missed all squared the 0 square would be replaced by square of course of dealt is much the smaller then experimentally accessible things we know all about and land is not horribly small itself which is not expected to to be for example the Higgs Boulevard and this is going to be a big thing and typically bigger than the starting next so this is a problem the problem is you start was something which your measured relatively small small somewhat scale small on the scale of the cut and then you get a correction which is far bigger than the thing that you were that you wanted to get out of here so that's the problem as we discussed of fine tuning and another way to think about this infinity Mr. think about property or leave find diagrams being integral Over the moment that they could circulate in the low P it is getting too much juice from very high momentum particles flowing around look so you could even think of or cut off at small distances will you could think of a maximum momentum it comes same thing the diagram called quite radically divergent which means that cut off scale goes to 0 it diverges is to powers Oliver Our OK that's that's CDs the problem remains bars Barzani now it let's discuss it the propagator for firmly on all the architects a notice made a very small distances this feature reminders dealt and would not help you particularly when belt that is very weak capital is very small This is just approximately 1 so it doesn't help you very much The New anything for you our but now let's I think about firmly on the school wanted from and discuss the fine diagrams of firmly on a similar pattern billing difference Is that the law granting the premier and has a different structure so rewrite the Lagrangian for firmly armed with discussed it before further Dirac equations grungy governing the Dirac equation and actually sigh bar will be Forex again that's action will be 4 x sidebar sidebars just basically the complex conjugate of side is a complex conjures times were again the matrices damages still worthy of the Dirac matrices sidebar bar and then there's a gamma of gamma Dirac matrices for Dirac matrices not important this argument and there is a derivative with respect to x new side there's only 1 derivative the other indexes soaked up by the jack this is structure of it we can also put in need and side notice that it's not Square here it's just in I let's check off 1st From this let's check what the dimensions of Sciarra and knowing the images of Siler can come back to this turns and ask whether the in that appears you're really has dimensions of Mets we do it the other way also but the from here but what eyes the dimension dimensions of an action or that of the dimensionless this has to be done so far I don't know what the dimensions of just brackets side inside star complex have the same dimensions was no different dimensionality between science so where are they have we have 2 factors of outside dimensions of side squared and no late cannot fall off camera maker Caesar incidentally just numerical matrices ones and zeros so they don't have any dimensions at all and that we have the derivative with respect to x what about that 1 1st so as is looming fuel so fundamental society it's not the same as the dimension of a scalar field in fact it has been mentioned
equals 1 of only 3 hands on fractional head of FIRREA always have and everything about has happened In particular the dimension of the Fermi on-field is 1 of only 2 of the 3 here with what yet it is so but nobody I know what I want to show it to get the same answer right it's of check here if sigh has units of 1 of only 3 heads have outsized aside as units of 1 killed a amassed units of 1 Elaine that's what that's together while going of what times wave a falloff that's dimensionless I particularly in order goes here is not in squared it and stroke really is the next OK so signed 10 units of 1 all over link 3 him how about the fermionic propagator each 1 of us sizes units of 1 of the 3 have store Muster propagated the massless particles work Starwood massless particles this will former would go for squared well I don't killed Nova was a 3rd power of a proper distance between 2 points and this is this is dimensional dimensional argument there also Dirac matrices he also Barak in this indices really wonderful right it correctly although I have to to do would be to rely on a writer with its with indices you putt the 4 vector dealt up here time we're index New York but a gavel also with index meal and then you take component of the Dirac drugstore the river from the index here downstairs index here upstairs was married and I JRD matrix entering Of the Dirac matrix is not quite right get this is not the consistent ID it added an extra factory built upstairs so I have to put in extra factor Dr. she said that's in fact with Dirac propagator is from vessels particle but From for a prompt purposes we can just call this 1 over Dokic fueled four-dimensional reasoning and after no 1 fueled a basis doctor killed aim when the man's Turner's included again the propagated this is a correct estimate of a very small distances at large distances a two-game corrected and suppressed by match for the propagator was always a little bit smaller and the amount by which its smaller depends on the maps the bigger the masses the smaller the propagator in here but a very small distances it essentially correct so let's no asked about find diagrams with firmly on them but Cher In particular I want to ask Is there something about a fermionic diagram that might cancel the bad things that we discovered erased that the bad thing that we discovered about self energy diagram due to both on the start with this diagram we said that was Lander provided by Delta squared In fact although I didn't mention it De Rossa there are some miracle factors the numerical factors a computer both parties for for cracks were about the signing the signed this past signed as positive and it is connected with something that I think I mentioned less closed loop diagrams involving bows owns positive closed loop dietary laws here talked about a lot less here as a sign of well on tape actually go back to your thing they discussed as Leicester but don't we or go back through to the little argument to print a little argument and Woods due to I didn't invented by men and find and mature so it goes as far as I suppose you want to know the sign of a closed loop diagrams evil at see the plaster miners these diagrams simple diagrams like this a real real positive or negative I so stud 1st with 2 loops as just a product of one-loop diagram of diagram involving 2 closed loops just simple closed-loop loop story and could be connected the other things it's time for but just To closed loops and ask what a sign that as well as the sign of a single close Lopez positive the product of the positives passes if the sign of a single cause Lopez negative the product of 2 negatives a positive so tool loops side-by-side always corresponds to us positive airport now next let's cut open this diagram and I think about diagram which is exactly the same as the original except we switch the particles were switch in interchange Tobosa it's a plus sign that's OK was related to it closely related to to the fact that the wave function of 2 Fernandez of this is now an ordinary throwing away function not directly function and ordinary Schroeder the wave function was caught Schering just 3 of the wave function of the 2 particle System X 1 next to it is some under interchange of X 1 X is equal sigh Schroeder
anger of X to Annex 1 another Lawrence who just interchange the particles you just get the same way function back and that's a plus sign he firmly under exactly the opposite trend eons is also assuring away functions to firmly arms but to firmly eons you always get a minus sign and that's symmetry of the wave function to firmly also says that China put to fairly and in the same state you will always get 0 because if you have to firmly islands in the same state that's a symmetric wave functions and the wave function for friend arms must be this minus sign requires all Moon over their cars are all out of context wherever when you think the change to firm you get back exactly the same thing of course but With a minus sign in the quantum mechanical wave function the implication of that is that if you want take this diagram and switched from you would get a minus sign relative toward diagram without switching well then I'm not switching was positive just because it was the product of tools equal footing switch them In a diagram must be negative from HBO's islands switching and does nothing and will remain positive but when you switch the particles like that would you make is simply make all one-loop diagrams to look back and you cannot trace this around it really is just a 1 will play twist and it's just a one-loop diagrams and so the net result is all one-loop diagrams firmly and will have the opposite sign from a diagram for those arms and this is very general the 1 look diagram sons is positive the one-loop diagram preferred your typically negative as it as an example kilometres diagram which is correcting the man Our of Biggs bars on this could be the Higgs boson on for example it is bows on this positive moves lender where land is quartic coupling here where I think erased it from Lagrangian aquatic coupling times 1 0 without the square Mel let's AS suppose there was a firm Iran's take a supposing that there was a on which had the same mass exactly the same as the bows on he got hunger draw bows on the bottom line is that more less conventional bows and for some reason a drama about lines and firm eons with roaring is a diagram that could possibly cancellous involving Fermi let's go out diagram the simplest diagram weakened we can write down in which we think is bows on whatever it is its still firm eons kidding that 1 firmly on you can't have a bows on becoming 1 on it must become an even number from around so let's take the bows on it's still firmly on and 2 from Young's compact together again it looks quite different in this diagram but let's estimated estimated by the same kind of into argument 1st of all there's some coupling constant let's call that coupling constant g is another coupling constant g here this coupling constant is not the same as a lender in fact it's the coupling which involves the balls on times the product of 2 on fields of to determine Lagrangian side dagger sidebar side times by buying and side-by-side orders the Higgs bows arguably behaves bows on coupled 2 from the fermions could be quarks they could be let pounds they could do whatever you like let's take a cage farm where they will discuss what particles could be their moment for good at work areas who I I calculate this diagram well 1st of all of this diagram involved 2 point this diagram only involved 1 point now strictly speaking this point could have been anywhere base so strictly speaking we really haven't been able to do all all of space but now the bill is trivial it just says that the process could happen anywhere is space but at the point where the process happens and then there's no integral left the article absorbed at this point emitted from that point that he hung complicated the particle is absorbed that went pouring and emitted from another point but if these points are very close together it looks an awful lot like that's what we do with this diagram well we could for example hold the center a B average position fix just as we hold a position he affixed and nonintegrated Robles space we get all the average position 6 or even better we could just even easier we can hold 1 . 6 but then we have great sum of all the places where the other point could be so this would be the amplitude particle the be absorbed that a position and really emitted from the nearby position so you eventually got back integrate all over that point all you could degrade over the separation between the points holding the average position 60 the way it doesn't matter what is this going to get well we know whether propagated are propagate is all 1 over Delta Q is firm eons a look so each propagated is of a formal 1 over Q. There are 2 of them 1 our Dokic you as a fine diagram this is gonna be proportional from 1 divided by Delta the sex but later we still have the
integrate holding this point next integrate over this better a double D for
Delta and it will be for Delta well so leave that I left out the coupling constants g squared and 1 more thing I left out or Celestyn might sign elope of early on it's a local on so it gets on my nerves now how big go well when integrate between you integrate from very small distances namely little Delta to infinity is far for it to be far away but a kid it's not allowed to be closer than the cut off so this is an integral which goes from small distances dealt to infinity for each 1 of the quarters how big it the grow what warmly said calculated is again just use dimensional analysis is no length scale on the problem an integral the lengths so as not only a problem other than Bangerter integrating and of course the cover of this interval has dimensions what I upstairs 6 powers of dealt downstairs that means it has a dimension of 1 although Lane square and only possible answer is 1 divided by little dealt square don't just on dimensional grounds alone this is a B minus G squared what will then this is not literally an integral from this if there are 4 integral therefore integral Sears use each 1 from Delta to infinity sign changes if you like so no sign Fritsche compiled gap you could imagine integrating each component of Delta from some small distance will and Vera now there's no sign are in fact is no sign change into grants possibly noticeably in the good and the past is no way they think anything parts friends of mine so this is good BG square Over Gopher squared up this GE is dimension OK let's right check that let's check that works checked the bed mentions of G always put here it is GE find that the scalar field from sidebars press tour firm theorems and bows on scalar bows on the same point I let's check what the mention of GE has to be this says units of war following this says units of 1 of only few the product of these 3 has units of 1 of only 4 24 x makes a dimensionless so G here had better be dimension you color is a form of Yukon Copper coupling between the Higgs bows on for example to firmly on these couplings are also dimensionless GE is also the tumors and the answers again some kind of combination of coupling constants divided by the squared kind the minus salt Eureka get mightiness G squared on Darfur squared no instead sensor doesn't look likely made much progress we have a number here comes grab beastly habit minimum we have a potential source of a minus assigned to cancel plus sign but you would think it would be an extraordinary miracle if nature chose to make GE squared this coupling constant exactly equal this coupling constant here that would require something special requires some mathematical structure which would tell you some symmetry or some other mathematical reason to say she was G squared equals Calamba that's supersymmetry that's exactly what that sort of thing that supersymmetry does over and over again it restricts the coupling constants combinations that it turns out that those combinations are exactly the right combinations to get rid of these nasty divergent integrals on many of the nasty divergent world next time will discuss supersymmetry itself which is a symmetry principle which is mathematically very pulp and it tells you such things and the masses of eons must match exactly in the notice something interesting off the cancelation would be a complete if the fermionic bows on had different massive fly because the property wouldn't be exactly the same in that case there would be a cancelation would be incomplete but as long as the properties as was the efficiently system similar for sufficient close to what I've written here at small distances it we get rid of the infinity of the firm a lot of balls on didn't have the same message slightly different figure out work might have canceled wouldn't exactly canceled but the divergent part of it would cancel so that's the kind of thing the supersymmetry off proximate supersymmetry Dutch will discuss next time the method that will be about the mathematics of supersymmetry it's a very very abstract kind of thing but also use some examples of how supersymmetry operates always take care of these nasty find putting problems private property of hostile formal please
visit us Eckstein tracked down EDU


  772 ms - page object


AV-Portal 3.13.1 (abea844c86ad1b15ca76e1472346f3fd8bea123a)