Supersymmetry & Grand Unification: Lecture 1

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the basic ideas who will talk about this quarter who originated Our our questions having to do with renormalization puzzles and go up sometimes Fazeel's sometimes used for observations about the renormalization of the Standard Model Solheim prefer would be a good idea spend a little bit of time explained to you we've done this before them a couple of times but still are describe what renormalization issues at a combination of 2 things it's a combination of learning how to eliminate hours Of the description of physics things having to do with distances which are so small that theory relevant to be questions that you're asking the end result the other half of it it is very simple dimensional analysis back its learning to think about how dimensional analysis tells you the Institute some of the very difficult problems of quantum field theory that have to do with distances much much more than you might be with you might be interested and I this is simple examples of renormalization namely getting rid our car things such a toast Walter B. arresting 2 if you're interested in the nucleus and have a nucleus works you maybe you acquire a quarter of a fundamental underlying constituents of nucleus well for many many property to the nucleus is really a collection of protons and neutrons those matter much with most protons and neutrons and made out of a simple steps it is to solve the theory of quantum chromodynamics to discovery and to compute the properties of the protons and neutrons but then I wanted this with that will begin in computing the properties of the protons and neutrons you might mean there may ask you might spend a few other properties but also the forces between them also forces between you know layers of protons and neutrons move pretty slowly so there's no real need strong need for relativity theory basically the nucleus of is roughly speaking described by nonrelativistic quantum mechanics of protons and neutrons and all you really need from quark theory is that find out what the properties of protons and neutrons are masses spins and the forces between them what you got that you could forget where it came from and say protons neutrons and support forces between them but that you're interested Adams you may not be terribly interested in what makes up the New Glarus you use nuclear physics to calculate the properties of nuclei which nuclei exist which nuclei 5 what they in fact you is the comic physics not even very interested in the massive Milquetoast but still you my warmer a given nucleus of fuel of its properties not much basically just Metternich charge what you'll have the best on the charge of the nucleus you could forget completely where it came from Yukon forget protons and neutrons and you could say there are no nuclei either a 92 of them while more because I suppose but you start over again elementary particles with today's walks not committees but I if you would in nuclear physics of the atomic physics who say we start over again with a new set of elementary particles we forget quarks we forget protons and neutrons which started with nuclei 92 of them all however many of them armed class of course electrons are pretty small but we get rid of electrons is still be able to do atomic physics we calculate properties Our Adams Adams means nuclei plus electrons we calculate their properties once we have their properties with SARS here is a collection of cans of exist in major cocky arrogance Coffee Adams or chocolate Adams Fatah is full of various kinds of Adams Roger have you don't need to ask where they came from more well you might want to know all little bit more because if you have to calculate talk a little bit about properties of a matter for the proper Marchall's tonight but we talk about how you think about molecules are you go from Adams molecules but but In going from atoms and molecules it's the same kind of deal you will figure out how Adams bill themselves in the molecules want your molecules Newcomb more
West forget where it came from and stop putting them together and he could buy assemblies and build up anything from there so each stage you eliminated the things which was smaller than you were really interested and the result was a coarse-grained description perhaps not exactly description are far more useful description for your purpose as well the same thing is thrown in quantum field theory where you have feelings at all possible scales every possible wave Rory constitutes a degree of freedom waves of arbitrary wavelength arbitrarily small but describing physics at 1 point scale you don't really want a half to deal with all the things I'm very very small in scale which run stinker you you invent a way of summing up all of the effects of very small distances and replacing it by effective no parameters new prescription that's all the renormalization Rio years are back together With environment analysis let me give you an example of renormalization began its justice example of going from Adam's Mark yours from going from and our from apart from nuclei plus electrons food Adams and how you deal with some how you deal with a comic forces were with comic forces come from how they kind of electrons broke arms not not for Palm but nuclei electronic this is a classic example of usually thought was renormalization but his renormalization where a getting rid of these very small degrees of freedom also the very past degrees of freedom small usually goes with fast small a system is typically the faster it a motion to getting rid of Mali small things but also very rapid things goal of renormalization so let let's start with something win over well of Adams Syria Adams is very simple it's just no less Nevada electrons away I'm actually interested in is a pair of Adams they could be a pair of our hydrogen atoms with the could be more complicated than there are just some of Adams I'm interested in is describing we dynamics of this pair of Adams in a simple away the complex structure of electrons cloud of electrons or whether a complicated stuff well like those described by Mr. Blix to particles the particles call Adams was forces between them how you understand forces now the advantage that your half year which is an advantage is that they electron motions are very very fast by comparison with emotions Of the nuclei nuclei a heavy nuclei a thousand times 2000 arms the widest nucleus hydrogen nucleus is 2 thousand times heavier when electrons and bigger nuclei really more and more of sold you could almost think of Adams as a heavy bowling ball with a bunch of little flight surrounding it and rough why is moving very very much faster them holy war was removed is given bosses just not accelerate the bowling born much make an approximation and father 1st approximation use a matter bowling ball nuclei us so heavy that they don't overall or want to calculate is effective cancel the potential energy between nuclei between 2 atoms in a way that gets rid of electrons which gets rid of separately electrons and nuclei so I do you start route this is quite a mechanical problem as any quite a mechanical problem you start with a heavy fermion Hamiltonian is just another expression of quantum mechanical version of energy so they write down for you 1 Hamiltonian Iowa right down if I really wanted to do was problem arose 1st of all I'm not interested in our corrections coming from the special theory of relativity north here that's our arrest offer for molecules soft you begin with nonrelativistic quantum mechanics and that means the energy 1st of all consist of a kinetic energy Of these nuclei 2nd to nuclei abuse saying we could be for example are hydrogen I saw the momentum of a 1st look lawyers builds P 1 P 1 square provided by twice the massive look less Connecticut energy 1st loan glare the nucleus of the nucleus of the atom and advanced peek through square at the kinetic energy of a 2nd nuclear test and then of course the error is the call on forged between the the
code between nuclei class he squared the energy class he squared provided by the distance between them on 1 to score are born from facts are left our job image of dementia for wives and stuff like that registered and their what comes next electrons select some of everything because electrons everything that had that involves electrons 1st of all as a kinetic energy of all electrons let's call the electronic call a movement of electrons Q Hughes of ice all twice a math of an electron were quite small big mess from nucleus use
small for the electrons and this some all the electrons so Norway electrons their kinetic energy of forces between the electrons last hour he squared provided by that score little are I J at the distance between me and I J electron as the call on energy between them like static energy what I left out all I have left out there be forced between protons and electrons self that's 1 more turn I guess we can call arms minus square opposite charge track of my he squared provided by the distance between the eyes electron and you 1 of the nucleus Our nor the court left scores at our capital are 1 the RIT means the distance between the 1st nucleus and the ice electron and then another 1 the 2nd row from 2nd electron of our warned start to Tewari 5 there are things which involved the electrons and there are things which involve nucleus here all of these evolve electron know until you really I want private brought intuitively art 2 time scales he won time scale is wall Inc and has to do with the very slow motion Of the nuclei why the motions of nuclei slowly because the nuclei Avery heavy and they move around while forces in fact than never accelerated very much inside a young molecule so we think of them as very very swelled by comparison with the very very rapidly motions of electrons or much more rapid than they are so electrons former we're trying to get rid of that Laura replaced by something else well this is fairly easy to to do in principle concept to actually do it might be more difficult concept very simple you take everything in the Hamiltonian here that involves electrons Roper together think of it as really Hamiltonian of electrons alone but what about the positions of the nuclei for present purposes now we're saving nuclei moved so slow and electrons adjust their away functions so rapidly that in 1st approximation we considered the nuclei not moving at all their fixed nailed down stationary and we just fix them we think of this as a Hamiltonian of electrons in a fixed background fixed background lead and nailed down stationary nuclei so we fix the positions of the way I was the positions of the nuclei effects than this becomes the expression for the energy offer a Hamiltonian but still are function of the position of the nuclei at a function of the position of the nuclei but both can just be Yap what would from only guests effect for the moment we don't need we just say their mail bound the very very heavy Our when I cannot violate certainty principle and things like that because eventually will take those moment back into account and approximation here is just that they will slowly I only take this Hamiltonian which only involves electron coordinates and the fixed positions of the year of our nuclei and we solve it wasn't me we solve this floating their equations we solve the Schroedinger equation for the lowest energy state refiner lowest energy state Arafat more reported the lowest energy I Eigen value we energy the ground state energy basically the ground-state energy of electrons in the background of the nuclei but Coetzer PARIS core where Furman Stewart show us is quality he our although turned a Bob electronic electrons and what it a function feelings of function is the positions of the nuclei battle every also was taking care of the lowest energy state the lowest energy associated with me positions are far more and are too because of the positions of the year from nuclear now where we do next now we say OK let's take all of this and forget about it erased it we can forget about of course Markham completely weaker requested by the energy of electrons as a function of our nor too class he alright Travis Of are 1 2 Troy have now now we have a problem involving only the abrupt arms only nuclei you only the nuclei of potential energy between them that was originally there plus another
turned the energy which also Combie regarded as potential energy as a function of the position Of the 2 nuclei and therefore contribution of potential energy this is a way that week eliminate our problem electrons and replace it with something else in fact it's only a function of the distance between electrons and so all actually find is that the high on dynamics of electrons is some arrives 1st of all have called potential between nuclei but then on another term in the potential energy and the other turned the potential energy when you combine that with this term he gives you a force will give your potential energy which looks on right when our look where extremely close together it's completely dominated by the coal long-term here repulsive when a far away there isn't much energy between them and in between some some attractions and attractions Due to be electrons however we know that the think about electrons again for this our 1st hydrogen molecule or whatever it is we don't think about it we just have an effective potential between them we solve the problem of 2 protons potential like that we are the source of their work like the ghost of a bomb here it would be somewhere function and that's a process of No. 1 eliminating vast degrees of freedom but we can also call renormalization we started with a potential which was just this potential we got rid of the high-frequency degrees of freedom and the entire potential was replaced by another function for potential was renormalize that's a basic idea all renormalization is associated with that idea eliminating very very fast degrees of freedom and replacing them by in effect of slowly are a narrow lead normal from Franconia nor for a review doing your by next book such renormalization we want top-line at the quantum field theory summer show how you apply the quantity of what is it that you what is it that you get rid our what bureau you could even think of it as things associated with very small distances are you could think of things had to do with the very high frequencies of a short wavelength short wavelengths high frequencies show but the things or getting rid of the problem are the degrees of freedom associated with very high energy high frequency on worth Yao before we do that was just group whose dimensional analysis risible mature officers forces to take a break from an hour from renormalization theory from just want to do some simple but eventually result in physics and generally remained skills you need dissidents pine and vast and leaking yet rid of toward them in elementary particle physics by taking the food dimensional parameters of elementary particle physics namely age bar and see that miracle back tool but that's a specification of tool Our combinations of the of the scale of the problem of dimensions of the scale of the problem but it still leaves 1 by mentioned that you have to specify a one-dimensional you need warned quantity with dimensions and that mentioned Comey taken to be a scale once you set h Oracle toward a sequel The warned only one-dimensional quantity has be specified it to be taken to be a massacre be taken the being energy could be a momentum or commit taken be or taken to be a tiring but you need 1 specification art with is not measures here than the units of mass bracket means the units of mass are the same as the unit of energy white because MC Square ensues equaled a wanted man also equaled could be of momentum also drove that the units are Lady which we corax weight are the same as the units of Krajina us because sees people awarded for the ozone layer and final are not the the same as the units of White House mass and energy In fact they out in 1st the so-called 1 dimensional specification either Reulet on mass labeled kind but once you fix it were about to enter all masses have units of immersed Lane or moment that have units of 1st lady missile 4 are strong let's keep that in mind 1st but dimensional analysis we have only units are like everything your city town or met the pair horrific draft pocket let's not talk about a typical quantum field theory on Wednesday I think will start with a scalar quantum field theory and I'll show you what's entailed in renormalization we have a simplicity now just a quantum field theory was stable scalar field that's or wherever it has a low grungy and and from Lula bond we derive finding diagrams we talk about us find Byram's will better off and even set roughly what the calculation of firemen by removal look like ones on a a those runs here's a look around you for 5 it's very simple it's just the derivative at why With respect to your space subprime squared these things before us the kinetic terminal grungy and and then it may be a potential energy strategy my b of 5 which is a function of 5 now what early units of a Lagrangian deal a similar grungy or where are we do with around we integrated will you we use a low Grosjean in the principle of least action that's what graduates for as whole Indian classical physics Ernie case in quantum physics is used in the path of the world but basically in either case a quantity of real interest is action itself was actually turned and him as see in the grow although around you and the rule around in a while and space and spaces low grant you feel so they have nothing quantity which is usually called as some some factions or Samarra from hours as as for action tests Road sex catcher Northeast asked for action and that's the integral B 4 of around here are actually His always something yacht question action has units of each bar but a as set equal the warned so age farmers now dimensionless action is mentioned was no dimensions at all and that is what I will grungy areas it must have in the 1st way go before however a Lagrangian must have inversely Lagrangian density here must have been wrestling for the 4th power now what really after is the dimensions of the field itself far What is image of fire itself so till you figure out book Was it has to be on this trial here this term here derivative of fog with respect that X squared error has have dimensions of universally some of former 1st lady the boss this has canceled was before XTS before XOX as units of this
must have units of going for for well off or other units of Why are the units of the derivative of fiery argued the rearview and Sephardi I'm going the warned that a unit
of the derivative of 5 different cheating with respect the extras give you only immersed another square of this is just these dimension of fire square this tool and that has to Duane minus 4 and that shows you that these units Orefice squares must be willing minus to what the summarized 2 units Our scalar field the units of a scalar field I just in 1st Lane wait minus 1 good thing to keep in mind very very useful for crimes a purposes are that's an example of the mania of using some simple dimensional now what about the roles finding graphs or to talk about the rules of fighting graft better but 1st of all signed graphs or come from 5 fired might have things like habit far-right as things in it like and the square Over tool as just a parameter it really is of course secretly square of massive fueled by tool fire squared and then it in half things involving scorer G primed FIQ Connecticut have things of 5 4th and that of score coefficient of 5 4 4 and that traditional our our location where the 5 for and Horn on non-American all kinds of terms of it and thus noticed that these terms are also have mentions Pistons also have dimensions in fact the squared his use of like to fight Cuba's use from 3 and so forth so and from that we can read off for a workers dimensions of firearm now works she talk about buying the diagrams find diagrams are built out of vertices and the vertices come from a potential here G. let's see 0 yard you must have a unit of met wise amassed the whole thing a half have units of wave of minus 4 years later the latest 3 this must be in restoring but in wrestling thing was that right 0 gee would have units of mass farthest obviously has units of mass squared what about the dimensions of Lambert Mention West dimensions significant by Michalis coupling constants are especially important renormalization yours have units of mass square of course you inches what terms up here and you could follow with the images are OK now a quantum field theory all the rules defined diagrams of built 2 elements 1 or the other vertices and overseas are red off from potential here for example G 5 represents a vertex in which 3 articles come together coefficient of such vertex Texan a fine diagram is just G the fight for off fast for particles coming together this as coefficient GE FAA's coefficient what about him advice for it emphasize growers risible a particle comes in with crossed indicating goes back out I'm just broke but brutal crossed just indicate that something happens Vera namely the particles absorbed and readmitted and the coefficient is just and korda overture building a finding by that there was a value the value of corresponds be amplitude for processed a half an hour has a value building it off as the elements of the vertices and propagated a propagate as represent the motion from 1 point to another I'm so let's talk about proper leaders the proper years From 1 space-time point to another within this job was lying between us article doesn't really move along a straight line implications of particles Quantum Chemical but the motion from 1 point to another or emissions from 1 point to be captured point propagator I'll just indicated by a line goes from Aug . 1 of a number of tell you what the meaning of the propagator is mathematical meeting of the property a mathematical meaning of the property is just a amplitude of historic particle warned warning if you create a particle warm pouring that you'll be pet animal point but mathematically work corresponds Mr. starting with the vacuum of client field operator FREE an ad for scored X X the cause X what's closed wiII a mafia somewhat quarter of a point of point X import White so you've created a particle at X and now you want to remove the particle Hawaii so that might be some fire wiII creation operate a creator creation operator with him 5 x creates a particle and vigorous 2 ways you could recover works for the
A's action or what fire why aren't we brought them 0 creates a particle at White the action of 5 x year creates a particle 0 but this could be red create a particle at what's he amplitude that after a certain amount of time goes by by that you find the particle act why that's so that's
meeting about the meaning of this symbol here the amplitude you created a particle X Europe detective out water a metal the propagated that is will the propagator is it's just simple to do you create a particle attracts because wine but nothing has is this 1 of dimensions of the subject here where the dimensions of the object off the vacuum as just state the state of lowest energy aback humans and states don't have mentioned you wouldn't say of the state has a certain massed not the state is just a specification the euro configuration it has no germs but fire has mentioned fires dimensions of immersed Wang so what's the momentum of a softer and rustling squared if there is no match for 40 there late scale and the problems of Lujan just the distance between X White XMY would be the only thing which would specify any link scale of the problem so could you guess what the center would be attitudes quantity of were square board like will add on they were make sense when he won our X squared matters were ripped out 1 or more y squared now 1 of ex-wife you mean by XYX sexes of 4 vector wives for what I mean by that time the obvious thing is 1 all the distance between them X minus Y squared and the distance now means the Lorentz invariant the proper time of proper separation between them or X minus 4 square solo bats something we learn from reverential analysis that if there is no mention the problem with this article doesn't have a mail then the propagated is just 1 over the distance between the points not something important blows up a gives very big when the distance between the 2 pointers quote so the amplitude for starting at 1 point and detecting a particle of a very close point just on dimensional grounds blows up and beverages that's the source Of all divergences in quantum field theory that propagate have the virtue of Rikers backing cause affinities and problems just a fact the the propagator becomes will be gets more August answers OK every thing else building up find diagrams and calculating but they also of course interpreting focus so let's now start with the idea of renormalization and how what works was very simple context let's start with the renormalization of the masses not as that in scalar field theory of parameter of Pierce was actually the mass squared turns out the Mass rarely appears in field period only appeals by virtue of picking the square root of their square which appears in the dynamics of the theory is typically square of the maps are as do with the fact that energy use the square root of p square post and squared always and squared which appears so we might as well on asked about renormalization of em square Raza meter and how we do it so from this picture or here we see that let the interpretation of a mass terms is just a basic simple find diagram or Sobel vertex the diagrams where particles absorb at point and needed from the standpoint that doesn't have to be exactly the same point well with a microscope which is only good doctor lawyer we've built accelerators which showed study things down toward the scale of the minus whatever his 17th cm or whatever it is we're not really interested in the details of what goes on on distances smaller so if we can find a process in nature which would mimic this vertex even that protects might be separated fuzzy over a very very kind mass linked scale we might not be interested blowing arrives such fine distinctions anything any diagram which absorbs of particle and Henry emitted from a nearby point would be counted as part of the master in effective description in which we don't look too costly and were observers description where we get rid Of all the very short distance and high-frequency degrees of freedom let's go much I did maybe find diagrams it we can build that will this just a particle comedian and a particle going out Russell give you 1 of our 1st of all let's build it out of this protects all he fight before vertex Calamba protects it is a very simple process a particle From goes out but user-defined diagrams where there's always a crazy but still to find diagrams where a particle is he and comes back essentially exactly the same quarter Kovac exactly the same pouring really what's happening particles are going anywhere courses just being emitted absorber quickly think about this final environmental market calculated to give users should have used the rules for calculating at 5 hits the amplitude for a process in which particle comes in In goes back out and this whole apparatus you may be on such a small scale but we might even see it might be too small-scale for us to be interested in or what is this propagator this propagator it is where will direct propagated by race right now we're just 1 0 Weiss square but XMY have the same point in this problem was not exactly the same point mainly mainly over blurring distinctions banter some what's called a color scale factor set some very very small distance scale we might want to ignore separations on match small-scale what's called the cut from corn field theory cut off say we don't think about scales more Mack added it's so arbitrary thing to do what we could do do it Oh say we might be interested in distinctions on scales smaller and smaller in scale dealt then what should we put in here we should put in a propagator which is separated by this is no longer than we should put
propagator which separated by a distance Delta before interest on only physics on scales a little bit longer than that but we are not interest scale smaller window no we might want to say Let's calculate the finding diagram but Melina's vertex here smearing it legal but myriad In space smearing it over a distance of size of the role again I will get wild don't the squared the propagator 1 over the over square propagator throwing away all scales more window end what what I leave out I left out the coefficient Lambeck coming from the 5 4 when the Delta squares so what see amplitude and this approximation of particle become may be absorbed and be readmitted wells that Sharon has the original masters again happened 2 ways it can happen just by the original master absorbing its remaining it and then I can happen by the more complicated process and the couple amplitude van His original mass Turner's but given the no name in the name of court and 0 0 standing for original starting value and subzero squared or through plus just over a year or another way it is if you're not going to look at distinctions on such small scales for the effective mass be effective and the effect of mass is and North squares and square with 2 fast land all over scored Seoul Mr. an example of the renormalization of mass it's getting rid of all the grief of freedom on scales too small to be interesting to us too fast to be interesting to us and what they had to together wanting the to together it was singled glory effect which I will just make the lorry across continent goes out and amplitude require a chemical amplitude for it it is a North squared plus Y and dealt with square 5 such as this renormalization of or another was Macera a particle mass that you would see in a laboratory for experiments In which nothing moves so rapidly in software you could see where accelerator simply doesn't exposed more belt the effect of messages Yahoo North square with flock is is the effect turnover grungy and the effective mass and of course the land Delta square here this high season of the things that been America things in there so it's not just analysis the mature Alice's plus the evaluation of some integrals but most of it can be done by just much image for now OK so this is this is a shift in the mass due to getting rid of very very high frequency populations and some them are putting them into an effective description change investors will be called renormalize mess book off when I finished off we haven't evaluated every possible find diagram its but still another find diagram for the same thing Mr. works are suing did a is a finding by Rameau forgets forget it's using this supper a separate is another sign of diagram let's evaluate it also has a particle coming in and a particle going out but now I have something new we have 2 points while you do with those 2 points where we do those 2 points minority get rid of things on scales more well we basically evaluate that firebrand distance between these 2 points is again about dealt strictly speaking you might In the great over position reviews points what's even do that what's even think about that but we should think about but hold this point fixed misses the point where the 1st particle is absorbed and the 2nd particle is absorbed or emitted from nearby point a remember the quantum mechanical are always sum of all the possible ways of thinkin happened so With sexist this point the particles absorbed we should want to eat the great ensemble of all places where could be admitted or nearby places it could be admitted from so let's let's see what that would give us a we propagator is warmer or plans y squared for set Yafran particles I want yacht was still examining the effects all this chance Mr. has for particles coming together vertex so he is for particles coming together of attacks and he is for particles coming together and protects again but this diagram is higher order in Milan but still MX order and Lambert this 1 only has 1 where move Soviet land square With but as of now we look at this 1 over here this 1 will contain 2 factors of wonder if when that happens to be a small number you might say this was a smaller form a small Member squares but let's work out their initial typically be true if more member off but let's see what kind of things we get first-order get land squared services a order finding buyers grammar a 2nd or refined diagrams first-order find Bagram contains the coupling constant constant when quadratic and then it contains the Greek propagate is going between these 2 . but call a point of absorption here X and let's called at the point where the emission takes place what court X class dealt just work or why I work or X plus dealt that indicate that there's a separation Delta between the 2 . 1 0 a half we have 3 propagate is between these 2 points 103 as each propagated is a 1
over the squares right the distance between these 2 points is dealt the propagator was 1 overbuilt squared so this means worn or were cover through sex for said but don't must finish where I was particles a move X it can be amended expletive Kirkeby affords absorbed that Exacum admit it was dealt a boat really interested in the amplitude integrated over go all possible ways of this event happened particle being absorbed by Everex and being emitted from a nearby position in nearby position where we're not too closely about what positions and were not the right thing to do would the integrity man on Friday rules you but you could imagine that these rules makes sense or mechanical and always Of all the possible ways of going from 1 place to back all possible ways of getting from the initial particle of the final particle having been absorbed that X you could be emitted at any point X Force Delta but then you have been doing reopen fact was a duo Delta from dimensional and the growers are felt as a former actor figurehead everyone got where were adopted a sex but now we have a great adult devolve adult communities In the Rule coordinates before space-time coordinates right Delta is a force for want to integrate for rector have integrator was 4 components so I can write this down he governed ought be dealt at Delta 1 2 would you don't really in store for us just write beef us go back is evident in the world over a fell over before components of OK now where integrated between well we might want to integrated the large distances but not matter because this is going to be so concentrated at small distances are that's mainly dominated by when these 2 starter when these 2 points close to each other a store that sold the important thing Is the integral goes from small distances of water Delta the large from small distances of water store warren of integration here Delta each whatever quarter now you care to guess how big this the growers when there's is a dimensionless number it comes on the outside of EU member squared over here but by how can I evaluate this the odd be for all and that of the 6th round of 6 means land the squared Q yes but Mitchell and fierce we are not going do any integrals quest which is gonna say dimensional analysis tells us against the world was interval depend not just on the lower end of integration of but we don't taking good care of distances smaller than the car for means cut off from the field theory are off and we cut off the distance scales of distant spell the end of the list in the book and only depend on belt but there's nothing else for it to depend on Saudi answer every 1 0 Delta square fraught can so or get from here we get something that looks very much of course number here at the Savannah calculate more carefully as parties and other things service from commerical factor here but the numerical factors not terribly interesting for us if we tried your high-precision expanded it would be bought what we find this year this year is the same as this except land the square around the square and all of the square there many many other the diagrams which will also contribute 1 or adopt the square With higher powers of land for example is our but 1 will also give a 100 powers of when no 1 2 3 4 us will be romantic before off of some kind of others orders is when the cubes also thought we and the answer is represent infinite series of terms each with 1 over the square it's with square clashed with your friends on for example we have used this term year let's see what we we get from this from the fight Q. how they make a diagram With food OK this is this is the last thing we want more supple but Mitchell mouse what yet if we have an integral it looks like there's an interval from Delta affinity of something which goes at small distances like all said a one-dimensional and the gloom now one-dimensional and they will be dealt with what was quite as a library right as a logarithmic integral now on them this it'll ground you would look at this and say this has no dimensions of so you might think that it's a constant but it's not constant because it's actually a divergent integral whenever you find the divergent the good will more careful and intellect you just recognizes a logarithm and will be logarithm of but so on get in the growth which has as many power was in the numerator as it has in the denominator it's always a lot of that's a rule that they use very much but it's an interesting role on dimensional analysis and hit the bull with as many powers in the numerator resonance commentator always becomes a library is what powers the dominate a religious Jews dimensional analysis you would say that this 1 started work out our arms would you want over OK so let's let's this diagram here With of with this doesn't have a wine running down the middle composer told cubic vertices tho cubic vertices with 3 particles coming into which protects the source is 1 of I there are 2 propagated is a 1 or dealt before each propagator was won the squares the integrated and what about the vertices attacks is GE was G squared these 4 again we have the integrate of all the positions of this point keeping his . 6 4 absorbed emitted from some nearby point but we have to take into account nearby point could be so muralist on our some range of location about this or your 1st year we have as many
How was numerator Rozamond garment walk again we integrate from Delta 4 of us this 1 uses G squared logarithm of Dr. Joyce columns that we don't get 1 over square sometimes we alarm over the other possibilities also the single biggest thing but big when Delta small Warner called off distances more which is bigger 1 over the square OR logarithm is a very wimpy function doesn't vary March water is much weaker how well the Delta square built this small is very dominant over the locker room logarithm corrections of mass but the dominant things when the car off gets more very small distance cut off these powers these immersed powers of 1 with no squared right so this is called mass renormalization young yeah well over Arthur the other was a good question of course and whereabouts because tell you exactly a calculator let's just a lot of debate but above the point is if you change the base what does latter Lockerbie Geneva-based numerous a mail of constant and America multiplicative constant but didn't tell you what the multiplicative factors he occupies a lot of our anyway so that would be absorbed into the euro be a multiplicative factor he sold a typical calculation there will be some pie and ease and stuff here and by changing base of water a just change corporate so not always a dimension is a completely calm so just change America coefficient or in this case you're right here moved from case you right the point yet these genes have units of mass for what was supposed to be giving was supposed to be giving up correction something which is a mass squared of units of this G squared here is same as if as mayor squared that means the rest of will fall I say 1 you have sort of which Walker you can you can but you could also just Norris back this the same units and about so is an American number here that has to be computed by somebody with a little more power than were exhibiting here but there are you're right it can be absorbed into a two-year OK on that but the IPL mess that is given to what it is it is far more important for this kind of amplitude represents the massive the warrant for proper is now a diagram which particle is absorbed a location the middle Maria by is effective description of a mass of particles not cause is not obvious how this translates into the inertia of a particle so Our purposes now it's just a parameter or grant but was seeing that the renormalize parameter FTU get rid of distances it's more the certainly scale corrections who work in a mail well it's not just the mass that gives renormalize but who another I did just that although they still there were a lot by Iran's yacht silly of me he or death brought right already however learned this fall and may be that the series is a series of Bonds more and more terror my converge but still Bernie infinite number of terms and edit up then not yet layout flood bustle about the renormalization of land when there is also some gives remove much of the match circuitry normalized every grant you can also get renormalize but they don't may yes in light of more new lot 50th year they are also havel also cars loggers campers dimensionless because really along always means Margaret of built up over some of the scale of the problem but and I more arguing that the logic of confusing the real things I'm interested and they us confusing maze of amateur radio just expect From about work often what happens is that it is a water was really a lock our joke about times some energy scale and the problem with your interested but what sort of who are what it Laura B. Gilded Age or photo using her mix is Dobbins properties can still says it will only I got to the ball more go but I'm very good answer was more they Delta's integration variable other secular temple arms from a operational point of view experimental point of view lend the fight before there's nothing but the amplitude for particle 2 particles command and go out again Mr. particles and from an operational experimental point of view if all of this takes place again on a scale which is too too small for city you lump it all up into an effective coefficient of fight vital for 2 particles into particles out fight for I for for example you have finally diagrams wedge look like wish this will also contribute a renormalization fight before and that their work about the reason amok work that out of the walk away along it will give you a log off but each 1 of these terms here is something which in itself can be re- normal or so what's going on is the effect of very small distance physics when you lose some level I think it all into account the same way we took electrons into account when we are when we study modules for example we take them into account which salt for them we get rid of them do whatever has
to be done now we find some effective description which doesn't involve those microscopic degrees of freedom after the result is renormalization of every everything gets changed everything gets shifted are so a parameters of the theory but you measure on not the parameters of fury your input in a series of Mae West and of here you measure of owes which take into account all the shortest and physics on scales smaller Neukom state arm for early then they eat measure clue a lot of yacht measure has taken toward Carol by summing also find and diagrams involving leads scales smaller them with you concede it has an effect our work which is the sum of all that stuff which you like together you want together into a single thing but you called the mass squared over to the physical mass where the thing you measure and when you do experiment but let's say relatively low-energy thousand are really really small distance is this renormalize may last year which is the sum of all our job slows include let started any zeros there must be a vessel a yacht record Barep and ensure Brink but before we do let's talk about the real normalization of some other matches in narrow this is the renormalization of the mass of scalar particle you might think it works essentially the same way for a family and it doesn't very are better behaved bad behavior use you want a bad behavior in the forest and you wanted to get out he answer but would imagine your head but the call distance scale it's is something very very small have the cultists in scale might be the plant scale we might be uh we might there there be trying to account for all physics on scales between experimental scale all the way down Clark scaled always back members more plant scale then will we would put in the Delta here would be the plot points of punk latest terribly small 19 orders of magnitude smaller than the year sigh 20 orders of magnitude smaller size of off 17 orders of magnitude smaller than the most current up-to-date accelerator experiments 17 16 orders of magnitude got square is a very very small number in ordinary particle physics units for example if use then the plant dissidents would be tantalum minus 19 numerous and 1 Orlando the square would be watching the 38th mayor I attend the 38th for what can a mail account and so do we want to get for example for the Higgs boss on the Higgs Boulevard was an example of a scalar particle where can't so we wanna get will I something like about tool 100 Jedi 200 formerly getting getting think the 38 this is we the only way to avoid it is currently the signs of all of these things some of them may be classed some miners track for signs of anything and and squared itself could be negative or positive we want to get out of he answered which is on water 200 GUT getting contributions which are 17 orders of magnitude vigorous the only way that this can make sense is if this all of his cancels precisely because 17 digits the 17 digits assessed to cancel and leave over something in the 7th House Ali in the 30 s to cancel composed of our sympathies and 34 digits and we've always something I think it's in the 35th minute of 34 this is called this is a fine tuning problem on the Higgs goes on but just recall we know about the masters the Higgs bars are arms and will be north from big bows on as a potential for the Higgs field as a potential which looks like that near the origin and looks like Vice square all right but with negative coefficient I never told you that the North squared was part of it can be negative or positive but Rolando is assumed to be a number which is not much bigger than 1 now why why we assume that we should have 1st of all because this will be nonsense the terms your completely intractable of the numbers got bigger and bigger bigger are but even more than that we know that this kind of quantum field theory becomes mathematically consistent because the land or water 1 is as big as it could be really should be small were so sumo Lambert modestly small at mouth Webster Our modestly small but not tho not under which more no reason for very small and experimentally we know we can't because we know came because we know what the number of deaths last year is still a lot of them are don't work at stuff and we not that it pulls but it still has follows the number of times and all of your you have to go a long way down the chain before went the high power over Delta is a relatively small number start means that all whole bunch of them have to conspire don't from Russia a of some after conspired to give this ridiculously small answer only she member he lenders typically a number of water warned strand were right arm over his remind you were with marimba are we speculated the aura value because his good reasons we were going to them why the the potential the Higgs bars on 1st of all why has habit Mexican Hat shaved 5 hours in order to facilitate the problem of getting masses from previous symmetry breaking and so forth but off the potential typical potential would be of a former miners this caught muse call to rule by scoring off call it instead of calling and not square record brings new Square because it's got to be negative we know there has to be negative forget spontaneous symmetry breaking so fast again when the fight before and I might be more terms of the deal with terms of believed not to be important fire what if we where does the minimum of the minimum of Cairo's we
calculate the minimum by differentiating with respect the fight and setting it derivative equal 0 what you'll find that the minimum Agamemnon fight means square which we also called OF squared minimal accord resistance sincere efforts were also core ever scored back was equal the new squared or and if lives a number or order of magnitude 1 and so forth and
ever remember about half have for experimental reasons all the masses of the Z W bows on controlled by F. not only masses of Uzi bows on told us that death was about 400 g you find that tells us Revlon less land there was some absurdly different number and worn which should be that meal is also a number which is of order 200 read another Woods is mass terms of work 200 GUT even negative effect of of negative of work 200 you but yet it is composed of this ridiculous of terms every 1 of which is 38 orders a mail which could be his biggest 38 orders of magnitude bigger and the thing you try to get this is known as the fine-tuning problem sometimes called a gate hierarchy problems of a hierarchy problem the hierarchy means a hierarchy of mass scale from a plant scaled back the scale of ordinary of particle physics Norma's gap from enormous ratio of scales that is not just that there's a small number of physics the mass scale of white articles this is incredibly finely tuned thing which is composed of many pieces all of which have to something small such ridiculous in your Oulu understood that's ridiculous idea of our Farmer sometime early eighties late seventies when this problem was 1st identified and quester you go about it but before I guarantee that we talk about ministry normalization of other particles the other particles of the standard model and why they are not in themselves a problem it's really just 1 fine-tuning you don't after separately fine-tune the mass of the electron or sort things wine doesn't be electron have the same kind of problem OK so let's talk about the arms firm eons don't have the same sort of problems so us saw the master firmly on the Mr. Framingham balls amassed not amassed squared and it's contained in the terminal bronze years which is in the sidebar society sign of fermionic fields that described the creation a violation affirming on and terminal grungy and that controls of the defines the mass of the electron of quark or whatever it is hazardous has a form and sidebars your that order last for several Premier go 1st of all sidebar is also a terminal Lagrangian which creates a process where fermionic comes and gets readmitted absorbs firmly that position and sidebar so again it's very very much like this term here except only involves the masses mess square but that's not a big deal we can certainly Nagin diagrams which renormalize amassed from Russia you will now why it's not as big a deal for a solid year member I you a couple of times a girl with sidebar side is the thing which always absorbs a left-handed particles any mitts Our right the article or absorbs right in the article and that's a left-handed particles a foot you between him and Ms. arm of the EU firmly on the frontier was mowing down and bars an axis with a right he helicity riding in the spin relative to its direction emotion master more flip that's important thing now so this is the thing which takes left right or right away no 1 has could renormalize the rest of electron for example 1 of the things that we put in the standard model was the mission by the front on of a scalar or emission of redeemed balls on a national scale orders represent scalar bottom-line gage bows on this could require more like the dynamics and quite like the dynamics the only thing that can happen to an electron amidst a a gage course on a photon what happens today he and Mr. an electron when emits to gage are nothing for him this doesn't change Saul emitting a gage rose on text left the left or right right you could work that out from the properties of around here the admission of a photon doesn't flip be helicity of aid from what about the emission of scalar particle will allow the scalar particle Ellis fled from Rafah right or from right to left a gay bar Lance don't flip off scalar particles do swept the direction of rotation of electrons relative to its moment OK now let's look process to use which could renormalize the of Elektra a little bit of a surprise supposedly electronic starts out with mail notice in the bars are case reserve that even if they a particle starting with no merit it gets this huge commanders contributions From renormalization and the ring on the renormalize Maris is not dependent of renormalization of the masses not dependent on whether the electron had ordered the medium particle have amassed 1st place is always terms would be they even of story now let's take a case of electrons so what kind of things come we have here is electron Mormon alarmed could be me Evans or photon number definition of a best practically by the Commission on recognized as and amplitude Woodfall left to become right all right because of experimental point of view of terms was recognized as an oscillation between left and right we get left going tho right can happen and let's suppose starting nest of electrons 0 begins with electron has being 0 is 0 anyway you go from left to right well you could amid a photon absorber for part of photon always takes left the left or right right and no way by a sequence of emissions of the absorption of photons the make a left go right the conclusion is in quantum electrodynamics or any theory which only involves the emission of gage bows arms from Iran get Norway mass renormalization all they get no mass renormalization so of electromagnetic energy of an electron if electron started mass us if it started mass where's the correction would be 0 on massless electron consistent flooring and pure quantum electrodynamics model pure form like the MX a massless electron is a consistent thing that starts Alan S. Lewis beat bearer Harvey starting point the input mass it will stay that way white because photons emitted and reabsorb will not work from left to right what about supposing now there's a scalar particle of electron couples of the Higgs field was example suppose that the Higgs field can be absorbed and remitted sorry amid rivers or what kind of things that make fanatical left Goto right now I can't because the scalar remission he always takes left wears it always takes left to right or write is scalar particle here a scalar particle although is involved tradition is uneven go from left to right alright but then in the reabsorption he Robak collect and think about it the matter
how complicated the find diagram news it's always good all involved in even the number of vertices because involves an even number of whatever gets must get reabsorb that's what comes out of couldn't be just electron ghost electron whatever gets into must be absorbed the number of vertices must be even if the number of vertices even from this and the our Our than you can't make a left or right and so again Skelos emission and absorption will have no effect on the mess of electron from 0 OK can you would ever get a shift of massive electron for example or more yes it is yes but only a few spot with a mail was master a massacre of as a vertex and find diet and which does take a left a right of the coefficient is proportional to the input maps so let draw fire Bagram which does create which does show from rest of electronic voice at the duo is and and absorbed photons Foothill here I have 1 of these Mets assertions which itself were from left to right the could start the contacted right but then the Masters takes you back the left also that right left Costa left and the master and takes left right and the right to write the value of this fine diagram contains 2 factors for 3 factors it contains the electric charge twice the fine diagram of emission of photons is proportional to electric charge the coupling constant are charged of this kind of diagram what have you include charge school where but also has the original starting man original starting 4th Court in North so we see that the shift in the mass is proportional to the mass itself so now we come right out of massive electrons will consist of and not class something of 180 squared times and Norwalk plus more complicated diagrams he bought times and in such a way that of the stunning was Europe begin where it would remain the implication of that is that not the starting this was 0 there would remain 0 it's that starting this will vary swore it would remain small you would still less questioned why is electrons for white compared some fundamental scale but at least you wouldn't have this problem you would not be canceled our our differences between large numbers to make a small number the reasons I don't know remains electron may be small and or corrections to it are even more so firmly arms the Mets earns better behaved very narrow scalar particles were but these northern as well gave aren't have the same property of the star out massless I won't go into it the start out restless remained restless all orders so what that means is that understand that the mass scales of the Standard Model fine cooling problem is really only 1 fine tuning problem it's a fine-tuning associated with Higgs balls on if you get that warm right all the other ones will be OK because all the other masters on direct response to the shift of the Higgs field dollars we erased I guess we are for the shift of the Higgs field the shift of midfielders control and doesn't the go this enormous renormalization shift office of huge amount everything else will be OK all the other for the would-be nor the fight the only fine-tuning the Standard Model nor really you are crazy for a only really crazy for the masters from the Higgs boson which has the B about 30 orders of magnitude smaller and wherever fundamental scale you envision off that's a great puzzle that supersymmetry and the other kinds of theories like that are intended to address army roughly speaking the question is is there really kind of context where the heat bows on cannot get a mast correction which is enormously lodges any kind of theory where the Higgs boson I'm itself will also be of particle was masses isn't driven toward enormously large values but renormalization so this is yes we announced our are there's 1 other fine-tuning extreme fine tuning in physics person is the only comes into play the when you start thinking about gravity before they think about gravity if you don't think about gravity and it's not a problem it is a problem that's associated with renormalization and that's a problem of the renormalization out vacuum energy renormalization of vacuum energy are also a serious problem also a fan over vary serious Our need for fine-tuning and destroyer visits with doses were dealing with fine-tuning on 1st what the energy of a vacuum areas for most purposes in physics doesn't matter why not well today and the constant or energies empty space has energy so be it but there was long as when you air particle it heads the right amount of energy that's OK OK as what we would be vacuum energy doesn't play role and fixed the real point is that only energy differences on port was examined difference so when you think about the mass of the electron both think about it as a man of the energy electron think about extra energy that you have he had a vacuum wherever the vacuum energy use your at a little energy when you an electron sows energy differences the energy difference between the energy of an electron me and your back your which is really what we call a massive electron SoHo fails then the vacuum gets its energy shifted by a large amount as long as Everything else get shifted along with it that's wrote structure or combat shares in a minute just sport what's happened from vacuum energy the vacuum energy issues something which is also normal argues that its renormalize by diagrams which have no input and no output particles Limoges vacuum and vacuum the effect of such diagrams is renormalize energy of a vacuum bottle can that the vacuum you know physical significance but nevertheless what's best for looks like so for example in the 5 theory and the 5 for a period of 5 years off or yacht but struck diagram from a 5 4 victory that involves no particles in or our particles of vacuum your areas for particles of the vertex here and that's how they use by a reporter numerically how your Weller contains Lambert and that it contains a propagator from he and back to the same place as a factor of why would total squared left derided factor while double square of separation aboard but then there's another 1 here which is another way square the whole thing is what would go for every diagram magical right down will typically goes well with built before us times more complicated warns but also cause while would go before and so the vacuum energy is also something normal because they get free normalized means that if you really want to be 0 0 you better find told the very hard precision but on the other hand who
cares workers we don't care where we don't care what goes on till gravity becomes a port and the reason is that In standard theory the source of the gravitational field was energy ever vacuum as energy it means that the vacuum itself empty space gravitates when i category now of course has to do with dark energy it has to do with the cosmological constant talk about Burma over time but yes this His also something that has to be fine-tuned has refined once again who enormously high precision are so it really strictly speaking to art school fine-tuned problems of physics at least 2 we know about 1 of them is the vacuum energy which has to be cool something like a 123 does more places and the other Is there a really Higgs mass which only has between December 30 of 35 best places of that these 2 promises in many respects these are these so biggest puzzles and particle physics at present time gossip may turn out that these puzzles are simply boot will misstatement of the problem we are often happens that her really really funny puzzles go away with state problem correctly but belonged times these problems were were identified and nobody really knows what solution Soper symmetry is a potential solution could be for the fine-tuning of the Higgs boson is not a potential solution referring to the year cosmological constant so the next time and prior apical queer with my arms for copper questioned prefer next time I'll start very little bit about what supersymmetry now the to get death those an what is going on on Zoe others does a good fire a shot in the arm we can talk about all the contribution of the masses I'll be part which comment from fluctuations of wavelengths from degrees of freedom down some very small distance scale have will depend on that scale who will depend on that scale so the real question is order quantum field theory how far down scaled we expect the makes cents before it becomes nonsense also molds solos frequencies are real things that we think are really there because quantum field theory makes sense them scales that's a subtle log back from what effects are saying is if we have some scale where we expect the physical change could be the plant scale it could be some unification scale we have some idea with his exchanges and the physics down that's scale contribute some contributions and I will only be bigger at support only be bigger this is Kira lower bound will you chills the Delta practice practice you choose Fidel where are with this this down to which you think you understand physics present prime so we have standard model the Standard model appears to make sense of very very small distance scales we talk a little bit about unification of coupling constants me by our coupling Council seemed to track together and they seem to come together at something like about 10 of the 16 while a lot of us think the for scale are aware quantum field theory continues down beyond that 16 g fever even smaller scales only get worse if you believe the quantum field in the model makes some small scale for state and perverse exchanges Europe whatever then you're obligated to state where the effects of all the scales in between what they did the theory how they renormalize theory and what cancel the more out there can only get worse by thinking about even more scales so right so we think we have a pretty good understanding of physics jails which are many times smaller arm and weak interaction scale ordinary weak interaction scale we have a good understanding of it only goal if we can explain what happened to the Mets contributions and the renormalization contributions from scales between the experimental scale and more small-scale what we think we're a mixture Johnathon's well described a sore lower back on how bad things could be with Delta we simply take the Beavers scale which we still believe the theory makes sense but was a year of baseball is east our probably more man we never actually be packed it in elementary particle all I had to put a face that not a dozen a dozen transformed the rotation of quarter the transformer returned a photon as a vector particle but described by a vector potential which when Europe a cordon of components of vector change the gravitational field is tens of particle headers simply state city and simple the scalar particles of particle with spin 0 nor angular momentum no spin angular momentum festivals for us for us 8 foes then you are or what O'Neal part of the bosses don't 1 there's a lot of things are it was a 4 all these particles called beat both on the very Samardeep deep emphasizing their very very similar Harrow who wore the report card they have Max worldwide auto fear that they are not however media both yesterday for the hit from that would require began the huge amount of foreign career actual answers are a little more delicate they involve various numbers here and so forth are infinitely many such turns some of them positive some of the negative and the other one's summer ones from firmly on and negatives of North America from both on positive West masses of the particles of coupling constants were varied delicately match we would cancel matching them as were supersymmetry supersymmetry does exactly that cancels out there will the question was why from Iran's involves arms questioner Norton or something for the question know it is that released the simplest find diagrams a vacuum energy firm eons negative the simplest a corresponding Bagram from both sides as possible and impossible ever firmly on and both on had exactly the same masks they could cancel each other in the vacuum energy but if they have slightly different masters minimally yet again these quantities here With huge coefficients which may be proportional to the the mass difference for example of firmly on both on by the hour drop for different coupling constants your have the find tomb in many cases still work together to work out that's what supersymmetry some arms 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