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Supersymmetry & Grand Unification: Lecture 10

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begin work for might subject for subject grand unified theories S U 5 particular there are many many things of core grand unified theories and were not from the starry all of them were discovered take apart 1 version of it and our see with what it is that makes the tech what some of the problems are and if I have time to discuss the connection with supersymmetry where charm he does exist are tried to you in on what correction the connection is not some deep claimed that supersymmetry grand unification of all our grand unification and 5 about supersymmetry not as just that it put both of them together you get a numerically better fit a certain things anyone by itself OK so I should begin with a few words about group theory Grand Unified Theories wherever they are are based on Group B group theory expands BSU Udo cross you want standard model a and it Fitch Corvette the grow pursuit recourse to cross you wonder if it's very Constable eat into group SU 5 special unitary transformations acting on 5 complex variables but before we do they wish to say a few words about group representation the particle multiplex former group representation that means the symmetry groups among and scramble among various ways off and hit before you could start to classify the particle that the article multiplex you have the classified the representations of ropes OK replicate the reputation representations of group sought to begin with as talks start with OSU you when always an employee in the case of a future war as you too has to do with speed are not you UBS should not be of the weak interaction BSU to arm the rotation of space CSU to what happens to be very closely related to rotations of three-dimensional space caustic statement of the same the the same bringing could enough not for us arm as you truly classify the spin representations of particles the angular momentum of particles are the angular momentum of Adams will be angular momentum of anything that angular momentum Collins in different kinds of multiplexed there's single which is sometimes just cost Gaylor because of doesn't transform on the rotational role and that corresponds to spin 0 Visitors center which is the spin of electrons have been back corresponds to spend a half and there's a rub there is a R yes to a group representation of S U 2 for every integer and half integer multiple our before every integer have spin 1 spend 3 have been too was good for our work comes next 1 8 0 0 1 who have warned was due Warner have free apps that have fortified their success In his daughter prepared by their own represent group representations and they correspond so sets of objects that the group acts are and mixes them out OK let me just tell you are a little bit about group representations although will really need for S when the basic before representations called the defining representation and just columns column vectors in entering sworn 203 for up to to the infantry altogether In units they are complex entries but given names of coal and sigh 1 side tools I worry about that about site areas and the grope as described by matrices special unitary matrices which act on pastries and make some up course makes multiply by Constance your pockets so let's defining representation and how money dimensional as it it's a dimensional now the 1st and simplest thing that you could do to 80 of a defining representation of S U and Mr. Peck its complex conjugate another take the the collection injuries so I want star to press for what's give reasons names misrepresentation could even called the defining representation or just create and Cup award representation because we usually just and representation of dimensionality in which has acted on by special by defining a special unit unitary matrices nite take it complex conduit to star about rock stars Our make receives which act of signed is
active on to get mixed up by matrices what's called a mule matrices precise star is acted upon not by the same matrices but by the complex conjugate so the Tri-Star actually transformed in a different way even sigh itself they formed a different representation from different representation of called the complex conjugate representation as Riverside Hotel you that of particles the states of particles transform under me and in the states of impact particles among themselves under a complex conjugate which is called get Ban complex conjured representation so 1st of all we have been representation and we have fluid will with some representations over here In the end associated if you like with particles articles crockery next whilst could your teed off shit ready for them if the Centers for Disease it defended the and yet refers size of the matrices the size of the board of this size all the pointy representation is also a library a room of a right from the finding representation of the same so the defining representation if the group assist you win the defining representation in the image and the unitary matrices are in my in matrices nite could construct mock-up and in that sense that degree and in the end bar on both individual representations and it's a matter of complete on convention which 1 of these you think of defined in which 1 do you think of the complex conjugate of defining representation closely connected to a fact that however began particle of a particle B and particle of back particles of particles so it doesn't matter which when you call particle which were new cornerback article want you name it we stick with OK the next thing you could do let's suppose that these columns here represent the state a possible states only single-particle again they could represent the spring states Hopper bound they could represent proton or neutron in them what's called I still spin they could represent the colors of quarks red yellow or whatever the appropriate Garner but degree of freedom there's not really have a particle here and it can have any 1 of 18 states let's put another particle right next door How many states are there and were only thinking now about be internal quantum number associated with the group as to where we're not thinking about position moment 40 minutes spin right now if each 1 of particle can in any 1 event states are many states can commit to particles 2 years of point clear and squared bird so there must be an 8 inch squares off a Toronto part and work which she wore could talk all said this particle over here and this 1 was definitely over here to a different location we're just trying to do the mathematics of group theory but pictures sold the definitely different locations on the a blackboard was no question of the being state because 1 of the mail them over here who want new memory how they suffer for saw a photo mean right right the palette exclusion principle would say you can't put 2 particles In the same state of being put in the same state entails not only these internal quantum numbers but being the same place I'm not explicitly tell you may not understand quite were here and 1 of rare want to say that there are no further constraints of exclusion principle they are not the same place they don't exclude each other in many way salt shit on over here we it could even be different particle types these could be 0 1 set of particles is Kabila mother but it just happens that they transformed under the same individual representation at Idaho Thomas state just with respect to assess your others but the position the angular momentum more of a interesting quantities but just pushed back with respect to this end niche called end of a particle honorific I could 25 and that's that's correct 25 25 such state edge and kind and in Square OK now you could label the state's if label estates of 1 particle perished sigh ART could label Red 2 particles system has sigh of R J psi IJT XIII runs from 1 year to the SII J. runs from 1 end squared a few at eye injury run over and squared possibilities as off example they would be the state's I won 1 in which both particles are 1 state Uribe's I want to sigh want show where big particles this article in state won this particle mistake it would be sigh 2 1 that would be adopted this particle straight to the article state 1 the get no exclusion principle of operative here direct square possible and high-value transform these things you transform them by thinking of me 6 J. indexed separately rotating on the road perimeter fact a simple with think about it Mr. think of this as as a prop up sign I of course fight GATT the particles described by side was formed ratified Scott is Querida introduced then how does the group act on this collection of things might acting on shiny and 5 separate worry rotating sigh and rotating fires so that the findings and squared the dimensional representation of the group but that representation is not be reducible noteworthy reducible optimal word wears irreducible mean what it means is that there are certain combinations of Shiite J. which transformed among themselves and don't get mixed up with other combinations of linear combinations which transformed among themselves don't get mixed up with the Oberly linear code with the other combinations so they can be pulled aside and thought of as a reprimand are really give you example of moment but let's just talk about what this would mean for ordinary spear we have to spin states each 1 labeled bite you are poor Darren array of altogether for states up down up down up up up up and down up and down back for a 1st date was not talk about up-and-down quirks of talking about spins pointing up spend pointing back right now is tool have been
particles if you combined to have been particles a report possible states but before all possible state among themselves or multiplexed what were the what multiplexer for states 4 hero 1 combination as a single and same which corresponds zeros and the other combinations is a truckload of states which forms morning spent a half an hour and a half from forming 0 always been warned what have understand that From the point of view of Shiite right now so I I get sort of as a function of close friends can be the symmetric wandering the change injury or an isometric Of course it could also be a linear combination of symmetric an empire symmetric but let's consider it also IIJ which are cement that so rare few the change on injury will become saying independent configurations is that 3 3 8 linearly independent combinations are in question about symmetric prayer worker correspond to a correspond up op that's America found them and 1 or square tool pop down Obama froze over 3 which are symmetrical with respect to the change and they have the property that when your act with the group as on them they mix up among themselves but do not mix in the last 1 the last 1 being or square up down minors Dow out the aided by symmetric combination services a cement truck combination and from estates or that the linearly independent want to reach a spin 1 multiple so when you take to half spends 1 way of combining them can give you spend 1 of and the other way it is unique because only 1 in combination to top down my was paramount it's a single and that means it just transformer group at all with 2 scalar With respect to these group provocations that give you users euro spring combination so this pattern you could take objects which transformed Paris not present in the and so what we call at a cross and sigh IJT is an object which meet in a square or in cross and across years simply means with combined 2 systems the across lot we can take the cement plant combinations and they by symmetric combinations they do not mix with Java the group operations do not mix and asymmetric symmetric half salt areas selected and can sigh JT can't buy some book hacked later how from earlier them Vero Beach carting are but what you do the camping hard capric every member armed this is usually are smaller representation this 1 sigh IGA symmetric and sigh J and another tool distinct representations and so the next thing we have in and cross some that and aid across and aunt by symmetric what's called pursue some examples of this kind of thing was to her will work out for you were kind representations of time next were already said that you can take that is a complex conjugate representation that could correspond to a particle and set 20 to particles down to study we could put a particle and and from a bar particle and the entire article this is different than a particle on a particle the question is what the group theory well what's the representation that describes a particle articles from many states or there is quiet again right exactly and squared and again there are 2 ways of combining their
mothers there may be more 2 ways of combining them the now there a relief and squares Oregon squared you can combine them again symmetrically Orient by symmetrically not to appoint him and shot back take these 2 things you of you right 80 works give a different label to it because it doesn't it's not me and squares came across in ah but there are still can't squared independent elements begin are described by some matrix MORE GATT this is also a matrix This is a matrix but you discover when you start thinking about the working out the transformation properties but they really or only 2 independent combinations 1 of them being the trace source combination and the other being everything else we've seen this before we've seen it in S U 3 where I told you that our vectors a representation of S U 3 which is 8 by French to free which is 8 dimensions instead of 9 dimensional a particle quark animated work and nite possible states but those 9 possible states committee and a single it and the rest of them correspond trace equals 0 or and trace this equals 0 and those form of what is called the adjoint representation of the adjoint representation as I mentioned in squared minus Her SUO free and squared minus warned is 8 however corresponds to be a cool warns of raw of quantum Crum by was a fresh you too Scobey adjoint but but but where's the adjoint representation you too three-dimensional the corresponds been warned us to 3 hits 8 dimensional call the adjoint representation but badly was 1 more linear combination mainly just as 1 that a single back a state which doesn't transform group girls sorrow this is although we need tonight a bar were representations Raptors representation in which is a fundamental defining representation there's a representation in bar which is the complex conjugate and Yuka multiply them together which is really just a act of putting down different numbers of particles of particles oil group theoretically that combining the representation together and in sorting out and finding which combinations will transform into each other are Group Co so separating transformation properties in 2 different representation and that is the process for example of picking 2 spinners and discovering that they conform spin 0 Osborn 1 three-dimensional representation or 0 the Aurora one-dimensional representation suspend 0 the 1 dimensional representation in S U 3 similar kinds of things at you fire the same kind of thing so we will see how this works by explicit example the group that were interested in his S U 5 S you find mixes up 5 objects which what the corn what's called just started be firmly on which firmly on his who will soon more the fur guns belonging to a single family there free families Over firmly Iran's unknown and are only 3 years probably correct artist remind you what the 1st family consist of consist of our 3 quarks took walks up and down but each up and backcourt cons in 3 or each court comes in 3 colors so if red yellow world Red yellow also there are Taiwan's electrons and its corresponding neutrino the a neutrino free slept on type and thorough this pattern gets replicated 3 times will just refer to to 1 of these
families sometimes called families sometimes called generations are 1 of these families can't nobody has a unified theory of how reunified together with different replications of the same pattern that is completely beyond us we don't even know what it means I not work means we means but we don't know how you understand why our art so let's just focus such a combination particles feel quite so what off the 5 entries easiest just the right down what the 5 entries for the defining representation and and explore Ooh but about it just as you would push for S U 3 you would put red quark yellow quark lukewarm 3 entries as would stop where suprarenal S U 5 mixes up neutrino electron which our writers he minus indicate that same mega which are stored end with Ray down by 4 books which 3 of 3 of the recorders novices and bizarre being the combined together but as you see it makes a lot of sense of quarks Orient works to be specific and only the noun quarks neutrino and electron they formatting multiple under the group S U 5 was goodwill press you find it's justified by 5 major cities which makes these things up among themselves transformations which take neutrino tho electron electron retreat know we see those already U tool or the weak interactions PSU tool of the weak interactions makes neutrino with Electra now about the things which makes me and died d quarks watches the color grow red yellow and green star b transformations which makes up these things here that's just car quantum chromodynamics but now we have new possibilities and we have to explore those transformations which take neutrino bound by down quarks electron standby down quarks so for something you know remember that fit each 1 on these Armed mixing up short call on this typically a gage bows on which are allows transitions between them the gage bows answer which allow 1 b quark Goto another Dick awkwardly bark or were mostly ignores orange the storm or about the guy gage boson owns which they go electrons back and forth a Of those W. Farrand so this is a corner here that corresponds to weak interactions and this was a bigger corner across bombs as you Tulia and as to three-year where you want was hiding will come through our I'll put prompt will say was prior to this the defining representation of restraint Norwalk works with worthy of quarks our 1 other point which I mentioned last time we always treat the particles as left-handed left-handed particles what about the right-hander particles electrons the left-hand electron comes together with the right right-hander away charmed will the interiors that effort particle is left-handed or rougher particles right here it's In fact particle is left him so we could always the numerate the particles by enumerating only left him particles for example for Burnham rating electrons we work enumerated not electron-positron proper left him that electron just from L. next to it and the left-handed positron laughter and applause at the end that particle of the left-hander positron is the right here and Electra this is just a notational device sorrow of lady who way of enumerating particles but because these groups that we're talking about do not turn left in the particles in the right particles and so forth so we keep track of the particles as left-handed we'll miss any that worry 80 we just have to remember that we were looking for the entire article for example of the d quarks and by Cork eyes this is D Cork but the left-handed is all left-handed and they form the basic left here the representation of us you find that were all the other articles that the Fed would probably or write them with are all left-handed particles most of those left-handed neutrino that's the 1 we see in weak interactions as a left-handed might this be Boris freely and then as a left-handed plus some this is no particular order here and destroying more than as a left-hander positron or about the left-handed deport D B B 3 because of left with Ferrero left-handed b quark former missing missing the up quarks are left-hander up quarks also left-handed and by quarks Bora Bora up borrowers if I have everything I have electron-positron that's good left-handed I have D Bach Watson quarks and I have up quarks and thereby quarks what's missing is a nearby neutrino would not comment on the question of neutrinos but I will tell you that the Standard Model for pure form of the standard model does not have an additional Web score of left-handed in the trio a left-handed versions Our sorry the right candidate version of the neutrino the In fact particle the left-handers left-handed neutrino and our right here In banditry know there is no right he and the neutrino and whatever missing 1 of area the gap OK this is a collection of eons in the 1st family of the standard model and that always OK so let's see which ones with captures in the five-year neutrino electron bound them OK in a winery group bound for 3 years a a a a a man hostilities laughter right now and how does it also a further not changes into the particle
of the same pens or order talking about neutrinos all the other particles but electron not electron turns into an electoral left in the electron becomes left right he and electron otherwise it would violate charge conservation of the left in the electron electron became a positron trying something bad happened charge disappeared for this is big for comfort for calm on but the mass is a transition between left and right in the particles of the scene charge same electric charge not only military doesn't have an electric charge so it's only 1 which conceivably could have a transition from neutrino and buying neutrino for Congress was has to do with neutrino masses the Standard Model incidentally the neutrino is strictly mass West Bank which is not the experimental fact experimental factors neutrinos have very very small masses extremely small are measured in fractures electron volts so OK the questionnaire was where a work to do we were Australia us about this yellow think about the transitions which can happen between these particles by virtue of emission and absorption of deed Posada now we're talking about S you 5 which is bigger than S U 3 courses to cross you 1 so there may be no kinds of start 1st of all there are various transitions are interactions that take place just among these To electronic and become an electron for example if met a neutral gage calls on the trio could become a neutrino offered emits a neutral gage bars on an electronic could become a neutrino if emits a bubble you might say so in here we have the weak interaction the weak interactions emission and absorption of W zee and also photons electroweak theory that's what's occurring in his walk in here and here we have deep quarks becoming Bach works perhaps the 3rd 1 he makes transition of the 2nd 1 or whatever and that means the emission of glow gone which will also let the think about a slightly different way think of the glow on team it'd be bark goes through the D Corky when it turns around and trying from using our a metaphorical language times around time it becomes a d quark and sold me quantum numbers Of the on here have the quantum numbers of a D D bar system particle and they particle another words they belonged to rule with respect as you to read where that I In cross and bar the adjoint squared minus 1 members of the adjoint gloom want is an object which lives the adjoint representation quark or APEC workin this case belongs to three-dimensional representation arrest you crazy but there and those things no kind of gage blows on half to exist now it would like to try to unify recourse just too close to 1 in testify mainly transitions which take these by these struck back and I'd be cool electron work this would be the emission of something while the charge of weaponry that's a borrowers a charter a 3rd as well charger minus 1 for marriage right for their demise for 3rd for 3rd 4th urged as what our charter for parents and I can never remember whether this what is called the X for the White House on its 1 or the other I do not remember which their Expos and I think this was the Expos on but I cannot remember XIY the Hawaii is the thing that makes be bar and makes a military however what Sarah charge Yao one-third of our my has a one-third charge one-third I believe it's called the White but I may have XMY backward I don't remember mental look it up before class but i urban graft it was the X and Y bows on which of the newly gage on which take quarks and make electrons lap time to make works were also was also the that particles of the Expos on which airs charged minus 4 thirds and the and that chronicle of the Wii which has charged minus a 3rd Bozo the new things will have to contend with understand what they do and understand what the potential no kinds of interactions are we course the possibility of a new kinds of things in nature do they disturb every everything we thought we knew about the the physics yes we do but will see quite so that the gage owns and the gage bows on live In the adjoint witches we then cross In Moi but the piece of it which has traced equal to 0 another words a piece of it which has dimensionality and squared minus 1 not comfortable with this and squared minus 1 just ignore it just and squared build OK half His Kosovo after troops give you 1 extra particle Warner 25 big if I further and that the expo at the Expos on and bonds have called White deep particles these quirks would be barred courts have collar electrons don't and we have to conserve collar the Expos on among white was armed must have caught that means that they themselves can eat and absorb Beatty like the quarks are strongly interacting things which combined together by glue on exchange and so forth so these particles are among the 4 particles which carry cholera and like quarks and never completely released
freely in reaction they always come together combinations with things over themselves have integer charge types of just like works in that respect for baboon this more than half the firm Iran's earlier but welcome parliament another thought all want 1 important point yacht 1 . 4 electric charge be quantum numbers of particles the theory like are related to the generators of the group generators of the group are be traced lists permission matrices and by and trace was permission matrices which in fact are in one-to-one correspondence with the adjoint representation theory are we generators of the group are trace was mission matrices independent Racal submission matrices or their dimension and a In square miles 1 so I actually generators of the group are in one-to-one correspondence with the adjoint representation the fact that generators of the Guber intimately connected with gage goes on emissions on 1 or 2 generators of the group has to be a source it must be a quantum mechanical operator which represents electric charge an electric charge is 1 person's fault are included among other things that can be emitted here we're talking about a theory that contains electric charge among the generators overgrow among quantum numbers associated with generators now was only 1 thing that you need to know To understand why I put bar there instead of something else and that's that the traces Of the generators 0 the traces of the generators 0 the implication of that is that the song Of the charge of summer's the quantum numbers within a given representation always add up to 0 that is a general for for a special a S Win groups from groups which are defined in a way which our which generators of trace 0 Trice the generators having 0 trace always act connected to touring terms of Utica matrices that was a specialist specialist means determinant 1 for the you'll lose that means trace equals 0 the generators tricycle 0 is another way of saying that every quantum number that's described by his group within a given multiple it must add up to 0 could surpass I had put the deep court here instead at pilots a up the charges of all the injuries charge 0 minus 1 minus to be bar has charged Myers a 3rd book and furthermore those or you could not in bed are electric charge into the generators unless 5 if you try to put year but be Bob electric charge of minus 1 and then 3 times plus a 3rd so the charges a up to 0 vats are there's a mathematical well it's a mathematics Hawaii would be barred in order to get the some of the charges of 0 OK now let's talk about well OK let's talk about now will be other firm Iran's which we left out so far the mystery construct another representations this is just a bit odd gymnastics to do the group feel your Serb or ways to do a group theory in a way that Burke easy to explain witty Dill you could try and build representations Mr. the End of this is the fight Mitchell representation defining representation we could start taking things like 5 crossfire and see what we get from a good thing to do but the something slightly different I'm going to begin with the fiber bar and multiply by the fire bar so what's the firebomb final is a collection is column electorate describing the impact particles Of this collection this is a this is a 5 let's write down what 5 Boris With the 5 just a that particles and dietary back from a D D D let's not worry about the hated were not worrying about now hidden in this world only worried always thinking about group theory just as the trick for doing some group theory I'm not consider fire bar cross last yeah people are so sorry it plus thereby particles we just as if they were just oyster mathematics now because she how group but representations combine let's consider the 5 bar cross 5 bar cross 5 bars to describe it we could make a matrix we could make a matrix on centuries ago if I by 5 matrices but I kind of want through a seperate 5 minutes into Toulouse and 3 next song Let's have some mom partitions to visit the White 3 by 3 toe by 3 3 by 2 just go to guide then Webster some labels such bar crossfire Boris we should label horizontally across here Roger for exactly what Isiah neutrino by drama plus Dee Dee Dee armed neutrino electron plus D B 5 bar cross 5 bar and also I also want the partition these things optional but with a 1 3 4 5 1 2 3 4 OK now imagine only to be imagined that has nothing to do with the truth but let's suppose I made some can't positive objects in each 1 of these entries I will put can't pass an object which has the quantum numbers of the tool of the role of a and
let's see what kind of object to make it all started 1 more effective 1 more affairs and I told you when you take the in cross and representation you could take it symmetrically and symmetrical saying With the Anbar cross and so I can't combinations are symmetric combinations were going to take the fiber below cost fired bar it die Cement Co and matter time at the 1st implication is that we only put we put zeros on the bag that means there will be no particles misrepresentation With quantum numbers of poem abactinal secondly the lower half triangle it just replicates the opera have triangle with a minus sign so they're not independent objects from the same arm of the same things except my sign and not new car particle states the only independent particle states go here here here here here here here here here here let's see what the quantum numbers are particularly electric charge will we use electric charge elected charge which goes here will be the electric charge of neutrino class a positron what particle has the quantum numbers of the of the cardinal was not just me electric charge what particle in the table are all of these havoc electric charge the neutrino an apology from the positron trio's neutral Solvay here in this place but he lost now all laser left-handed particle misses this was a trick to construct a group theory but we always be talking about left-handed particles all of this was left him OK where about the trailer bound quark chose neutral salt let's put here value court Mary core value for the free collars Of that war Mr. Bentley this year it was just an auxiliary construction we're not putting particles in the refined bar with adjusting auxiliary construction so I could show you what the fire bar cost 5 bar looks like with 2 races so don't be confused OK what particle has a the quantity electric charge of positron parts head for a total deaths have known all moved through me arms of firmly on here we're just talking about no we're talking about me on what particles have a quantum numbers of downpour among these all talk about which I construct do buzzer up foreign or to get up shop charged yet minus a 3rd is two-thirds a up or pursue 0 not you was about a generally quirk off for about a quarter if it's two-thirds not is two-thirds back caucus charge minus a 3rd who says charge minus two-thirds make and buy up for same thing here and same thing here that's but it we filled up all the boxes and we feel up this entire correction here so this entry harmony independent states are 1 to 3 4 5 6 7 8 9 carries a fine of course of 5 is called 18 in a 5 block across the 5 boroughs Quebec tend bar so this statement is at the same time collection of particles has the structure with respect to its quantum numbers of a fine if can bar this is actually a rather remarkable fact that the particles Fitch neatly into representations as you fire you may find it a little bit on Oregon awkward trapped a half the particles belongings 280 10 and Mitchell representations not half particles two-thirds of particles belonged to tend bar the 3rd belongs to be a fine if there is a bigger unification as possible into a group which is bigger than you fiber contains is you find called Oh all of these particles are in 1 representation of all Tam but you have to hit 1 more particle the North 10th see by article of the neutrino vote would like to know if we get told get to it but for the moment this is what's called as you fired unification particles Boca any questions of the young or a 1st in the desert for Otto Our 1st there is a a a a book this set of particles interim particles in a cement matrix a is that a away but not as just think he's an annual you like in line amount order quake but I don't think of it as a matrix are better think of a matrix but there's nothing to prevent you from taking them and lining them up Inter would take place but the transformation matrices which act on that where are not the full set of SU take matrices more matrices and our was said to think of it as a matrix when you start combining Inc representations together you could always think of them as columns of white despite taking millions amount calm but it is often much more convenient for think of them as matrices Sharma transforms matrices wrapped Transformers column was quite so this is said we breakdown of the particle multiple Eds the world body had more of you fire know how this girl Grove said role rural Surry Va young thank you dress how Soto Carlos considered collars concerned if we had a few hours or not Yao we
will I was cooked up with Mr. baby red green blue Lola Red Green who 0 red green both now what happens if you combined together for a green quarks a bloke quiet you get something in red while do however show so you would get an idea now solve let's say so user Miss and bike works here ah but still red with green would be below 0 Redwood would be green and the greens were blue would be ready tie Joe that's apparent arrester Fahd video questions but now this is quite extraordinary when you think about it you putting until 1 multiplex symmetry multiple quarks left-hander quirks and left-handed by quarks into a single symmetry structure left up quirks and left-handed impact quirks of works on the other hand with deep court particle and thereby particle left-hander particle emitted by particle along in different representation with the positron electron left and the positron left in the electron different representations and this neutrino silhouettes itself in the final with Nollkamper part was so Stewart with and tree that is B particle content for the Fermi on content on the Standard Model OK now Lech may wish that a five-minute break here you have a photo it's is really a EUR Otto pigs both from those who oppose below and our cuts across various the various kinds of pigs balls on cut across here they can take a left to right and were still going on and what take a find break let's talk about the various gage bows the various dates blows on correspond to the transitions between the use of fire of objects the same 7 gage blows on actually get that particles gage both arms in general have charge double sub charged Exs have charge so they also have radiant by particles are the gage bows on mix-up these 5 entries for example between him here we have to be Missouri W for car with jacket here and here we have
the ones know things that we have now are the X and Y borrowers arms and Jackson why bows arms taking this way he
X ever said look it up I can't remember which is X and Y and Y balls quite from my present convention to take you from DEBUG quarks trails because of a transition which happened by mission Of these particular gage How did those gage rose Arms Act among this tend bar in other words were negated bows on using made by 1 of these particles which 1 does it become out of the way to think about this is that the gage blows arms can be thought of as shifts in the case of some other gage balls on the ability of the photon for example picked an electron from electron sorter cut trivial shift which doesn't take way wears in this
column the wife goes on a shift to opposition to down
and the glow on shift your money blow supporters also think of them as curve shifts which if you around the space OK what those same woes arms grew were active in the small the answer Matt Eva take you horizontally or vertically according to the same pattern for example emission Oliver trade can take killed this readmission Ave Google 1 his glow on glance Obama he can take you this went a contiguous way that's the role that whatever the various gage Boris on due a shift that make the same thing is repeated here except that it can happen you could either he made a gage bows on angle horizontally war vertically another way to think about it is the prefer him the pretend wrapped these entries here really work can't posse of pairs of particles pairs of particles to be specific 1 of the particles or by particles represents the horizontal direction the other represents vertical direction and any gage balls I could be emitted from 1 or the other its emitted from 1 it takes you horizontally it's bit from the other it takes you vertically from 1 entry toward not so let's see what we are what we weak interactions gage blows aren't easy in the W for example do well with ship shift you in this opera was so let me use signal would be door horizontally horizontally they take you from this column of this column Morgan horizontally take you from this column of this column well that there is not much here to do the E plus doesn't do much OK but at what they can also pick you vertically From this neutrino slot through this positrons which means they can take you in this direction bound up want something that something that the bubble you bows on Gaza's W. blows on does take them off but that the art of B W boss arm is a source of beta decay found becomes Corcoran court is in fact yes and that's what becomes of up court inside nuclei and Dixon tried to a proton so the emission of the W bows and could take a downpour tore up Our that's going vertically The color Group acts among red green and blow he can act horizontally here taking in or another cholera downcourt for upcourt whatever color of up but it can also act vertically year taking this this and that mixes up the 3 you take green red suppose you might think blue red had they blue red well you've already here see were always remember this is really in and I have it I have put me entries trees over here Beatriz over here just a year are the negatives of the entries over here from Aurora man here a week ago from our blue to red on this side directly but ignore this way or ignore this way and that cholera acting on EU bar quarks although this it is the same as In the standard theory nothing new he know things I wanna get at his work was the exodus and the wife of what the X wise due on Monday this column he look at don't think do they take for example the Expos I can take an exam by particle could deal this entry to this century if you like that orders at that's taking this entry of this entry another words the emission of an ex are can take a deep bar His be coming along many on X and becoming a electron have he here left in these particles exactly the same kind of emissions can take place schlep calm between this is the 2nd 3rd 2 0 4 3 lately positron downpour but positron down quarter which intends of this constituent model year just takes this positrons bank work state and by being emitted by X being emitted stakes positron to bank war aum where else Krim happen but I get there right positron to Barrick work but see worker through 0 column don't forget such them core positron parser over backwater positron only that particle positron bound war that way you could figure out what the various submissions of X and Y both on top of the Y blows on the why bows on takes leave 1st entry to a 3rd entry at the 1st century wears a 1st entry personal here 1st entry 3rd entry down quark joining it by up for bank work to it by of course also over down work and hoped for are sometimes it helps to fill in the rest of these columns and their rows slots over here Pickstown court can't back up or so just got through it played little game of figuring out what the Expos on what kind of transitions the Expos a white bows on but they do exactly the same thing among these columns and rows over here dual he picked for example 1st entry the diphtheria 1st trailers 1st entry nothing here Kinkel go here for 1st entry 3rd entry 1st entry to the 3rd entry by means there no kind of process to used in 1 of those new kinds of processes vary very surprising sought Stryker will with the new house if further if the 4th and 5th century those of emission of glory or will you go from a blow told Greek work are her good a 1st before our 1st 1st before you Yao wife right there will be a 1 write-off for white goes on to dig then to and by off the expose on take drama of optic by I just feel 1 box a a a a a yard minus plus there right is Dedie miners D minus you minus you might use you saw our minus to you Barbie minus you bar green and minus you bar Ray that how water Java Durand where here right that's arrest of are table now it's redundant show 5 if a process could take you from 1
place to another here too those are the same thing appeared going roses that just interchange
rows and columns our so it's redundant to keep track of these put Ticonderoga to right caucus or mystery or a process which is unusual back 4 ships Brad quirk King Goto positron Quirk the positron positron backed by a bank court what bows on which is the boss on which a using new map Russia's text Expos was emitted then what's the charge of the Expos on the 4 thirds yacht 4 per hour not players for in this case it's the X minus 4 of which is being by particle VX we're talking about before call quorum and by but the X can also do something else see if I could figure out what it takes the 1st element to be start a 2nd element to the 3rd our reports Our 2nd element the 3rd element so it is a 2nd element the column and he is a
3rd on the Macomb here's another process to condone it can take up down up they had died it can take up with the Expos armor he but now was expose on nearby by Expos are coming in but by exports are from check that this set charge minus 4 Berg's Ed right away from 1 might 3rd tool plus 1 must of our charge might 4 now we take a minus for birds two-thirds now we get my news to serve so his toe processes that can happen involving the vase possible according to this theory let's put together we put together that we have a process in which bad quark because positron and it's an X That X no grabs a of EU Quark which then becomes an and by you Kwok what's interesting when Alex 1 more particles which is pretty much just a spectator and order another you quite a U court does nothing just becomes a court best a process which takes Our Deak work into you quirks with decor proton Rice's approach on that how Proton and creates our positron saying charges a proton and EU would end by you call or what kind of particles could you make over you would amend dockworker meant backcourt man's arms in particular pioneers Oregon's this would be a neutral climbers are coming out of I not neutral primers on Salt we've discovered of discovered but we postulated in doing this we postulated something than usual a process where proton reduced to the black box view of it proton becomes positron egg a Pine ought to another thing that could happen is EU quarter and quote annihilated make a photon this would be a little less likely be course there's an extra factor of the fine structure constant in New York and the probability some other process can happen Proton becomes positron and full-time now this is potentially are very very dangerous Our game therefore protons have a habit just became could become positrons I photons of positrons and I'm not needless to say we wouldn't be here are nuclei wouldn't be here hydrogen wouldn't be here so this is a rather dangerous process called proton decay and proton decay is a consequence of pretty much elite kind of can to you will find weak interactions electromagnetic interactions and strong interactions 1 grow as you 3 courses you took what yours of course warned group but product of sorrow of small groups to unify it into 1 nonprofit group we're almost daily fight every unification line all of which tries to put these particles together into a single malt purport or from lower which tries to put us your 3 courses you to cross you 1 together to a bigger symmetry always has proton decay is 1 of the consequences very dangerous not something we would want the happened to us certainly not something we want a happened quickly a because there were those answers say is that we don't know yet yeah was basically just refine structure constant your product of coupling constants where we're here for over here not different large numerically it might be a little bit different for a number of factors 1 of which we may get talk about but numerically is not important thing here is the order of magnitude of these coupling constants is seen as the usual coupling constants white because they all belong to the same structure we belong the structure and in this as you find fearing is only coupling constant coupling constant for the emission of a gage bows on wiII they wind up being different uh in our laboratories is something we may or may not have time discussed tonight drawn we are the order of magnitude is coupling constant usual coupling constants saying coupling constant which governs the decay of an Adam when it be excites the same coupling constants which governs beta decay saying coupling constants or bird cover all the or would particle physics decays so the question then is why this doesn't have to amend the blink of an eye as fast as are other the particle decays and potential and should not there are up answer because we've never detected reason we don't really know it's a real process Parliament but what leeway what do we have available manipulate slow down the rate of us that the mass of the Expos close and he has Garcia in the form of art 8 propagate propagator is always look like 1 games squared they may have some momentum dependence also with the momentum dependence would be require our momentum but that's generally small potatoes the important thing and Obama made here the mass squared Of the Expos on that would be 1 of
the elements and that you would have a product of coupling constant g times and the G G for coupling constant g square of some sort provided by X fight him next square now if you sat and calculated the find diagram for use a reasonably simple find diagram this is what you would get time some number OK a fight diagram gives them amplitude of quantum mechanical and put 2 a process how you calculate the probability for the processors square OK so there will be a G cut off water and MX falloff in the decay rate of decay rate is the probability per unit time for the proton decays indicator the question is how big the you'll have to make an X water that the decay rate of the proton slow enough so that it doesn't conflict would expand the question then is was the half-life for the proton Miss this is the decay rate in 1st half life of the broke upside down becomes our this His other factors in here factors of a mass a proponents so for purposes of this is the important thing if we measured Everything in units of G E mass of a proton this would be the became approximately order of magnitude stop bigger have to make MX in order to decay rate Warner that raises the question whether the bounds on the lifetime of a proton factors or kinds of bounced the truck Thomas clearly longer lived in the universe still protons around the Big Bang Proton bus Proton has to be longer than need to human being otherwise we wouldn't be there has to be longer than the age of the universe otherwise they wouldn't be here to make us so tend to be 10 years are 10 to 12 and 14th and the 50 years after sure but now the questions of experimental data on you can't wait around for a 10th of the 15 years to see a proton decay but you can start with Pinto the 15th protons us our protons a small amount of her small sample and see how war a decade takes place with 10 if the decay rate for proton the half-life of protons was 10 to 15 years that if you start with can't the 15th protons you want to see 1 indicate per year approximately 1 per year a proton decays is something which can be detected on a laboratory even among 15 of them not this is easy this really easy staff saying a proton decay heat a sample of 10 of the 15 protons and you don't see any decay lifetimes Lorna intent to a 15 minute put everything together that's not on the lifetime of the protons is longer than 10 of the 33 years tend to 33 years it was found on the FY from proton are once this theory came out was immediately evident that experimental physicist should be trying to detect proton decay the way they do it this enter the 33 broke pardons away for 1 4 woman became tent other 33 protons amateurs at 33 protons what's a massive tend 33 per cent of the 23rd protons is mall lover of hydrogen so this is the and moles of hydrogen bigger back there are big Arab mouse will be pulled by a bright right for the about but it does put that right Jeter for what a small number but Norway's New year remember we should Norway was years the required say fly brought that you measuring years had which measuring and like Fiat video like transit time across a proton so Skyview small number the expected lifetime if everything was a border 1 proton units would be the transit time like transit time across a proton donors your members minus 15 meters about 15 what 23 Myers 23rd 2nd wicket them then minus 20 23rd seconds is the benchmark number I can't the 33 years is the observational bound big number between Jeter thought it is not important right Miller did say busses end of a 4th November's big enough probably doesn't have the beat In order to be consistent with the 10 a 33 years is about 10 of the 16th GUB numbers 10 the 16 parties are red and the 16th 4 thousand after that stripped the right number printer 16 GTV those V minimum amount on the mass of the X and Y bows arms in order not conflict with proton Nowruz at a ridiculous number is ridiculous number 1st of all it is I was E 3 orders of magnitude more of media the clock it's not a barber plant that's a good friend 3 orders of magnitude the but there is another factor that makes this very very tempting discussed it before it's the running of coupling constants leak strong weak and electromagnetic coupling constants are not numerically the same
electromagnetic is somewhat In the with appropriate adjusted go our various factors that you for the group theory just for the group theory or the compare S U 5 with 2 3 cross and so forth from numerical factors numbers like three-eighths stream numbers but I'm simply stated with appropriate conventions all of the coupling constants in a unified theory should be the same but ASU 3 cost us it took quest sorry you fly is not asymmetry of nature it cannot be a truce maturity approximately a cemetery Richard why because of the enormous difference between the necessary mess of the Expos are the Expos on exists in the city multiply as the glue was the W bows on and the photon which exists in the same multiple and if the cemetery was an ideal on broken symmetry they would all have the same maps well thought I was a good deal light of than W. bombs on the globe on their messages of zeroing in the euro of formal court Cromwell dynamics of like the vote and now the Expos on has found this gigantic maps that means the symmetry is broken spontaneously broken What is it I guess it's not that all these that they're all aboard on of mass right you could arrange for them all have the same matter and not be 0 but that's that approach not really that OK what is it that gave the W bows on different for cars it was a spontaneous symmetry breaking while the Higgs Mama that created a different Mass W 4 and at the same time it broke the S U 3 cars to cross you B S U 2 cost you once what's necessary is a type phenomena are a different 1 different warned that led to this from the blitzes from theirs breaks the symmetry drastically between this block and that block and it is that symmetry breaking which would account the big vast difference between XMY bows on from a 1 and the gone busy 1st approximation all these particles are mass what they have the biggest mass years over 100 comparing things with enter the 16th G the 1st approximation this kind of fury these overall massless In fact everything on the black borders matchless and the extra bows arms have sworn to match sets fury and stroke to be passed so With a Mass Our tender 16 do you agree you find it's OK now what are the evidence do we have for a scale are kind of the 16 g we have a couple of other pieces of evidence the scale of 10 of the 16 GMT is the scale of unification was it means scale of unification means energies which are high enough that even the best of the X and Y balls are could be considered to be 0 0 or is for messily XOY bows on his 10th of the 16 GUT tender 15th somewhere between 10 15 compared to the 60 them well above that energy but sick can't be 18 due process trees are insensitive to the are they X and Y blows they can be treated as massless and that limit the difference between the X bows on the disease W and so forth is not important in other words of Volvo's ever Jesus symmetry is a good cemetery is a good solid questionnaires and what 20 at what energy scales does world appeared to be S you 5 and various summit wrapped answer goes as follows told you several times coupling constants are not can't depend on energy scales coupling constant that you see quantum electrodynamics fine structure constant actually depends on the energy of a processed it run terminology coupling constants run very if you plot in Stitzer traditional for much of traditional useful instead of applying the coupling constant plumbing won over coupling constants NU you plop them at laboratory energies misdirection you have energy and you plot the measured value of them at laboratory energies Andrew Walker a member of the energy here to plot the value of the free coupling constants which 3 S U 3 process due to a new 1 3 coupling constants they free number is the biggest value for allergies squared would be for the you 1 erodes the the weakest of the interaction of electromagnetic next year's your tool and next the year yes your race value plot how they run with energy in run with energy heavy cloud you don't measure if they run logarithmically very you calculate your calculated from the theory you have a particle content you have defined the diagrams particular find diagrams going to the running of his coupling constants and you plop them find you find do something like this however are that approximately what they do more or less come together look as tho they're going to cross them what you like Is they all cross at the same place would you like to say that there is 1 place where they all come together and at that point you
would say that's the unification energy that's the energy we you got high enough but beyond that energy all 3 coupling constants of saying no why they weren't differently why did they run differently if there's a symmetry between these 3 coupling constants why they run differently the below the cemetery started below this energy the symmetries broken a bond that energy symmetry is restored so that's picture you would like and you would like them all coalesced simultaneously they don't quite reflected missed each other by a fair amount but the tendency is certainly come together and I can remember whether this would crosses hero this courses he was matter they do miss each other by an appreciable amount nevertheless you take them gave them do the calculations you find our weapons if you allow 50 percent error you will find that these things cross at an energy of guess where are the same you can 16th tender 15 g unity sold the implication is that if you believe this theory the unification scale really should be 10 of the 16 g and then the massively XMY bows army would be about that are this is the reason now this fire that broke out in 3 years now but the John McCain who became by beta decay map you put that but yeah yes where and these right now yes but another mechanism for you right so you would young enough latest mechanism for it does indicate a does the capable climbers on apologize that women noticed it decays Proton neutrino and electronic trade so completely different process for the right are you could imagine a world you which the neutron was stable with respect to beta decay the new trial was a little bit lighter than the proton imagine that the trial was over this would be a disastrous World who wouldn't like it our revenue neutron would be stable the Proton would beta decay into the neutron take the neutron the New China would pick a by this process but again be life lifetime could be very long rights or just by juggling the masses of radio proton and neutron you could imagine a world in which just long life time when applied to neutron proton fight that's all that's pretty much it about time on that's pretty much it for what a grand unified theory is the only less than a promise to tell you is what we relationship between grand unified theories supersymmetry there's not a lot from you know what tight relationship 1 doesn't apply the other but what is true is that if you and all of the Super particles into the calculations for the running of the coupling constants then you do much much better How within within known about 1 per cent cross at the same place an accident as a 1 per cent accident will not be harmed in any case this is why there is excitement about supersymmetry in about grand unification grand unification quite beautiful idea of putting all of the particles and was single malt it like rests on the draw single group structure like there's a slight extension of the Syrians mentally in a fury based on the group 0 tape which is a little bit bigger than as you fibers to 5 bits and go hand in all 10 all of these particles exist a single the 16 dimensional representation of wrote Tan along with 1 of particle nearby nearby trees ah overriding neutrino was it usually called and that's a separate story OK that's the ideal grand unification the connection with supersymmetry which is not theoretically terribly strong but and politically some reason find detractors proton decay experiments are on-going Our life prime moves getting every year lifetime time get to you on or about right arm such renowned draws its power broker every year Obama goes up F supersymmetric theories the lifetime calculations different and can very old with a map but it never gets any bigger than about 10 of the 35 years or something like that it's difficult to make it bigger than the 35 in the Standard Model you can't make it a short with discount number firms unification scale you really can't make it shorter that about 10 per 32 years nothing you could do could make it short of a in supersymmetric theories it could go from a fraction of a 2nd and the 36 years an hour with with various assumptions about things so there is no real predictions supersymmetric theory for a lifetime alright May all your protons be stable and Phyllida Huntlee former court number which you worry for use of word sunshine if how how for
Moor please visit at Stamford . Edie
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Titel Supersymmetry & Grand Unification: Lecture 10
Serientitel Particle Physics 3: Supersymmetry & Grand Unification
Teil 10
Anzahl der Teile 10
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/14980
Herausgeber Stanford University
Erscheinungsjahr 2012
Sprache Englisch

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Fachgebiet Physik

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