Supersymmetry & Grand Unification: Lecture 9

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Supersymmetry & Grand Unification: Lecture 9
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review 1st a little bit about about symmetry breaking in general how symmetry breaking influences energy levels of systems and of course the energy levels as systems could be translated for ah purposes and to the masses of particles and where do that by a simple example simple from early example then I will show you how supersymmetry breaking works in a simple supersymmetric field theories that we were we discussed last time to discuss a little bit about relationship with gravity turned from what the implications of supersymmetry supersymmetry breaking par for gravity and vise versa and finally a 1st time I think we may start be production through OR for the GOP's the grand unified theories up a song symmetry breaking made their way very simple marble for symmetry breaking which really does tariff all of the physics of borrow more we walk talk about I felt like magnets and Gerald from magnets from magnets simply systems which are composed of microscopic magnets will not the worry about the fact that they happened to be in a chunk of iron that's not what's important what's important Is that the world was made up this world that exists inside the paramagnetic puts think of ourselves as being little creatures that live inside the firm magnet half of the magnet is composed microscopically even more microscopic them we are microscopically of little elementary magnets and will elementary maggots interact with each other a real from magnet they can't interactive each other at a bit of a distance to be of the nearest neighbor interactions are somewhat augmented by next nearest neighbor interactions and next to next nearest neighbor interact and so forth but are very simple mathematical picture of a from magnet is that each will elementary magnet interacts with its neighbors and if the interaction energy as such that it favors the means to lower if the 2 neighboring magnets of parallel to each other then that creates a firm magnetic they prefer meaning energetically to be and that paralleled that it creates did that from magnet and they could be things in between which have no magnetization called meaning to say that the magnets are very random fluctuating and don't tend to depend on the point in any direction or on the average magnets and buy from magnets bomb at rich let's imagine Adam In a magnetic field before we talk about things symmetry breaking of Adam Eaton a magnetic field what does and what does a magnetic field do Aborigine even before we talk about the magnetic field but just talk about the at nite so we Adams may have some angular momentum some spit at combined speed or below and so forth and you know quantum mechanics angular momentum only given directions quantized noses often drawn in elementary textbooks way which is somewhat misleading but maturity way see pictures of frequently chemistry books are where you have possible directions of magnetization vertically you plot some component the magnetization of these of magnetization some component of the angular momentum like busy component to pick up busy component why because as CEO but no was your arm and then you say the angular momentum could point in that direction actually comport Mac director Macomb point map erected comport map right to map and from about what happened polio of the directs a story of the important thing is that the order of the young components of magnetization components Our angular momentum along with taxes a quantized integer multiples but they all have the same energy they all have the same energy and that's a consequence of rotational marriage roughly speaking there is some merit but Baron here to offer roughly speaking a rotation can take 1 of these their actions of magnetization of angular momentum and rotated into were not I I keep saying that position Spears accusing him of Pierre our corrupt Tate 1 direction Our angular momentum of the Adams into Ann Arbor and of course a rotation should not affect the energy of an ad not what's the symmetry which says that rotations shouldn't affect the energy matter but thousands of victory as we believe in rotational symmetry of the entire Adam rotated the energy should be saying the implication of that the core mechanical implication of actors all these different states have exactly the same energy and energy diagram because of all the states have the same there or white true J. plus 1 of them would J is the probable angular momentum and they all have exactly the same energy now what happens when you put them indoor magnetic field if the angular momentum has no component are what's imagine we put it into a
magnetic field so this direction is not just directions but also happens to be the direction of a magnetic field are and if we Adams component of angular momentum along that direction is positive the energy may get increased of negative energy make it decreased and always levels get spot over their money and it's totally extra magnetic field magnetic fear what this from recalled a number the splitting of atomic levels of a magnetic field is a minor factor was an artifact right there was not only for over 100 years I believe I think our and Of course this changes spectra why news specter lines new spectral lines emerged it ever transition from here here while Bob rubber easily by transitions other states could be also up but these are important thing is that read energies other states which otherwise in the absence of the magnetic field exactly equal because of symmetry Split among themselves by a process of symmetry breaking by the magnetic field now surpassing that the magnetic field is actually do occur this from magnet that's going space affirmed 98 is an example of spontaneous symmetry breaking you realize that way in the U.S. The question which directions those a thorough magnet point data which direction when these energy is as low as possible was affirmed by the pointers this karadzic appointed any directions as woes although magnets are lined up the energy is the same and so there's no preferred direction that rotational symmetry all from magnets no matter what direction the point have exactly the same energy and his nothing else around the pick out direction space the only thing that picks out the direction space is the tarmac is these orientation of the armored so for that reason all electromagnets no matter which way the appointing off physically identical to reach other even from some abstract outside point of view of the pointing in different directions we're being nor difference between them for creatures that leaves inside from around however supposing 1 of these creatures happens to be and had an orderly Adams and it's under the it's interacting with the from magnets so here's a magnetic is the yet at the magnetic field of from happens to be pointing in this direction was wary that will have exactly the same effect as the external magnetic field just a mathematical magnetic field and it was quickly comic levels book them according to Lizzie component of their angular momentum but what happens if the magnetic field was pointing in another direction just as good a direction that way well from plant will be Adam was no different it's levels get Split it's not busy component of angular momentum which determines a the spreading it's component along the magnetic field exactly the same pattern emerges off it would be atomic levels but bikers salt on a federal magnet simulates if you like the effect explicit symmetry breaking explicit symmetry breaking would mean that the world was fundamentally not rotationally symmetric of course it is and that's that confirmed by the fact that you could rotate the hole From magnate and everything would be the same will words the symmetry involved not only rotating magnetic but also rotating the entire world's worth about Our magnet Vogel Mac somebody inside from magnet of course cannot do the experiment creatures made up of all expectations of a firm I could not do this experiment of rotating the entire magnetic field so they would say well bookstores like the world breaks the symmetry rotation or variants but what is the difference what kind of experiment could be done from inside the from confirmed that this was a case of spontaneous symmetry breaking rather than just the world being trucked a symmetric and the answer is the answer revolves around this phrase it we use before Goldstone borrows arms from remind your world from our starters 1st of all if you take all the magnets and rotate everything it cost no energy all but now supposing you do something a little different very slowly as you move through space solely means slowly in space vary very slowly and gradually you imagine changing the direction Of the magnets on as I could stay that way the magnets which are aligned over here about pull the neighboring ones in the same direction as their create so that a create with stores waves or a quarter of those waves are called Goldstone bars are but the interesting implication is that when the way it is very very long wave for an extremely long wavelength in this case they would be called spin waves on mag knock Magna arms rotations gradual rotations of magnetic the direction magnetic field both mag on them very very long wavelength ones where cost arbitrarily small energy longer their alas energy they cost because after all the way was infinite that would be exactly the same as rotating everything and that cost North G longer wavelength means low momentum and XI citations which have no energy old was energy goes 0 0 as the Waverly gets longer and longer cold nasalis mass of particles of the ones whose energy decreases as the wavelength gets longer long hours of momentum gets more and more sort of person living inside from magnet or perhaps too people living inside from magnet over here were he could send messages to each other but we believe we have wiggling somehow grabbing hold of their local grab ahold of all of the magnets rotate them but they can grab a whole hour Copper reminds me a bargain with normal little bit and the effect of that we're going a little bit will be the create spin waves or mag Martins and those that nuns can propagate from 1 from 1 person or another send messages with them and those people living in this round magnet after they've done lots of experiments with these spin waves will conclude from experiment that both spin waves are massed for us but caused no energy to make very very long wavelength 1 as if they were smart they would conclude that they living in a world of spontaneous symmetry breaking and not fundamental properties of the world erased that it's just that the world that they live in these energies are such that it tends to all lined everything but it doesn't matter which direction things or wine that's the basic phenomena our spontaneous symmetry breaking it does
not halfback necessarily have to do with but our rotations of real space Baker have to do with all of all of award In each of the internal symmetry groups of particle physics in particular things I guess you three-course you to cross you want for 1 of these things a we learned incidentally is that there's a kind of interaction between teacher forces and Goldstone Boris arms which has an effect which are calm through which are remind you of waiter but remember what effect the mixing up together are spontaneous symmetry breaking ends dg invariants was a ghost or forward extra class photo Gaylord became attract turned the gage bows on massive thing instead of massless and will come back will combat perversely murders were remind your that was the pattern for the idea of spontaneous symmetry breaking continue were spontaneous symmetry breaking was also an another mathematical statement warned to make the vacuum course being the state of lowest energy is just any 1 of these configurations where the magnets in this In this particular context of course From were all from magnets aligned along the same direction as it does a vacuum that directions a vacuum that directions a vacuum for that they're actually nobody in the world is big enough to get outside and make it rotates from 1 to the other so all of physics takes place in 1 of them and the people living in a vacuum in the world call back configuration molecular up at a ceremony vacuum off let's take the vacuum that they would a letter applied to the symmetry operation symmetry operations the generators of the cemetery or the generators patient cemetery the components of the angular momentum angular momentum sometimes accord J. sometimes accord held what's Court J. right now to consist of what we can do moment everything J I was J. do what where acts on a state it is that I personally rotates over there right infinitesimal euro takes a little bit yes the vacuum state were structure where it really was symmetric there really didn't have kind spontaneous symmetry breaking what what habit the what what happened 5 fewer if Europe Woodka Microsoft right after number yet this is this is the difference between Jay really represents the difference between the rotation number wrote repay state through infinite past small change In the state that made by car by a small rotation J. corresponds to a small change in the state if the state the vacuum state warriors cement then when you apply Jake if nothing happens the right inside 0 no change what ever in the state off from a formal mathematical point of view Soon spontaneous symmetry breaking is that 8 where vacuum doesn't give 0 it gives a State which is slightly rotated not equal to 0 means that vacuum has a spontaneous symmetry breaking the organist see that pattern repeated South in supersymmetry with the exception of course that the symmetry or the generators are these fermionic object 0 instantly what collapsed so let's suppose that J. on the vacuum rotate directive does not give 0 they want us give what does it do well that says an actor who gives a slightly rotated but slightly rotated warned is equivalent to putting into the system and infinitely long wavelength Goldstone bars are so you could say that on the vacuum creates a EU vary very long wavelength infinitely long wavelength Goldstar bars on Thursday on a vacuum change the energy not it just rotated the vacuum a little bit ends Jerry where acts on a vacuum which arrived here that gives of gallstone on state scored GB the Goldstone was on state and the fact that rotating the vacuum doesn't cost any energy appalled tells us that the Goldstone bars on has no energy this is a pattern thought more point woes point third-quarter lead magnetization of the pharaoh magnet it is described by Luo vector Our vector as elected each point of space so it could be thought of as a field its local properties of the year from magnetic and I will vector of course it is nothing but the direction of the magnetic moments of making up the direction and magnitude of magnetic moments making a prefer or magnetic thing called em that's not the same as core capital and capital and as a vector the points along the axis of the year before Palmer if Enders you'll that Kabila cases for example In a warm paramagnetic if heated from up then the magnets of fluctuate on the average was no net magnetization and quantum mechanics it just may be that the quantum fluctuations wash our magnetization if may cause you're all that's a situation where we say the vacuum a selected there was no magnetization if 18 com Paul program is not equal to 0 that's another way to represent spontaneous symmetry breaking Bernie complies with the enemy is not equal to 0 the system magnetized along the direction and if you rotate that component compliance with the law will become nonzero factor of busy component is non-zero and your update the paramagnet BX component may Command 0 what a white component may become a 0 so all of these things are mathematical and physical cholera works of the idea Our spontaneous symmetry breaking now let's review our little bit about supersymmetry Hungary and a little bit to it we're not there I have missed torturing you yet tormenting you readjust or little bit if we wonder what we got direct let's just review we worked out AT symbol a single example of a supersymmetric quantum field theory of supersymmetric field theories are good 1 fermionic morning bows on on-field motors remind you of Paris it involves 8 Super field by called capital fog and capital flight had the property of being a Cairo super field I won't Bobby with definition of that now but the important thing about the Cairo super field is Back in 1 form or another but it is really only depends on 2 variables white and
favor end of this remind you just the equations steel wire was equal ordinary coordinate X passed by later bar stigma favor don't call the coral super feels that awful complex it's important that complex and if you wanted to try and make it real what you would find is supersymmetric transformation would generate an imaginary part so it's not consistent supersymmetry real ballast fight and we introduced our grungy info 5 1st the super Lagrangian whistle-blower bronze I think I indicated by a capital where and it's a thing which you will integrate with respect us based space current then with respect to a faded 1 Turner was integrated where the bar respect fate is end their complex conjugate Court for greater bar all indicate explicitly that it was an integral overbooked failures in the bitter Boris entered in this simple example that I worked out for you lender it was
just a tough fight star I kind of I heard I could do it again the undiscovered tell work came out all weapons what you do not more fire was was just right there were far I woes if I was a sum of several turns the 1st Jeremy me an ordinary scalar field the next Jan being offered on-field French stayed on and the last turn called at times they made at their 1 favor tool are our yard think about these freed components of a super field fight side in the 3 components of a super hero of you plug back into a formula here and integrate with respect to the figures was integrating with respect to favors means means picking out Norwest terms of the expression when you multiply five-star times fight you will get a terms where Ford trader they the bar later bar when you multiply these together you would get a terms with 4 figures all together and you work it out carefully keeping track of the details what we found was that this became just ordinary action fora a scalar field an ordinary family on-field Aurora's gave rise actions which was the integral D X hot what they have have partial or fire with partial by star with respect to x new partial try with respect x or that's just the ordinary Lagrangian June offers scalar field Barnett and keep track of detailed numerical factors receives before if we very back with respect the fire we would get a simple Klein Gordon equation next there was a turn sigh Va our Cigna derivative of Shiite that's just the client that's just be a Dirac or mass force firmly on we're Grosjean and finally there was another terms which was just at star white just star aft when you square sword multiplied by conjugate who get a turn at times of star later paid Paderborn made a bar so that's also here that's all we got there and that was a starting point to remember what we ate to that In order to get some interactions and semester and so forth Sharon with said something that only involved society and not fire start for example fire square re-entered Samoa grungy or pursue program by squared for example now fi squared has no data bar dependents it only has stayed at the if we tried the integrated all 4 components of data we would give 0 3 0 a right thing to do with this case is just the integrated with 2 favors data talk be squared another oyster pick out the term of 5 squared which has to think so much I had to do that more generally we did this be effective it was to give us a mass for the particles such review from last time work it out in more generality instead writing fire squared here I'm going to write any function of but before I do any function of far-right let's be a little more modest for moment and just take flight and power with later Iran can get together terms with different powers this is off a firmly jet fighter and we can an different ends and make a Taylor series expansion for a function as long as the functions Taylor series expandable so let's take fight and put back in he added Beta and see if we can figure out what kind of ordinary Lagrangian for the usual further fighting side and F come out of it this is not hard this is pretty easy but I have to do each time all over again because I get confused so let's just take a foggy class sigh data Frost F data and multiply it together in times RKO multiplied again and times 5 precise regular hours after they have faded multiple I'm up up up about 5 or sigh trader past F favor Amalie looking for Will looking for the terms which have 2 stages only terms which have to favors Will be interesting because those only ones it survived when you integrated over fate so which cut terms is really only to turn this year only 2 kinds of terms nor was multiplication here which have to think it was the 1st comes said multiplying our product of societies with 1 F pick out 1 or the FCA and multiply but will remain 5 countries such turns and my this and in terms of prepared this after complete this Africa because septic a brick any 1 of them and then multiply by all the remaining 5 Sasser terms witches contains end times f times a fine to and minors more young vitally and minus 1 right a mere truck and then and that's important and fresh now but we just with Theo turned is that it is a term which is product our product of 2 sizes and all the rest 5 through size and all arrests 5 countries such terms are which is many times and minus 1 or 2 another year or 2 In times and minus warned or 2 the fight me and minus chill time Siad side Prime's side of something size and deadly you also have the air a complex conjugate so we also ever complex conjugate service book ever let write for you and a slightly different way what is aimed at times fight to be in minus warned yard where fight to ghetto a a a rare here it 1st of all a toe not
1 of factors as F E very Mr. new U.S. for when you when you go to integrate all the data it always picks out the tune with 2 right OK and this adult doesn't mean well but that doesn't mean equals it means that the term with 2 fade those picked out uses some of these 2 men battered plus a complex conjugate plus a complex conjugate fighters another later right there so but it's exactly the same strength but let's worked at it but it is times fight me and I was 1 of the original Soper pretend this is called super potential incidentally was called the Super potential Soper potential our right it v were ready so wrong Our substantial looking weary but a function of refined and in this case it is just a fight Vivienne from this particular case well as these fight in what is In times fight minus warned Mrs. fight here is a little different than this fight this fight here is just a 1st turn from Super field this video fires of formal expression involving a false Oprah field both the function V is the end parlor then what is it In times variable to me and my was power Mr. derivatives it's the derivative so Wicker right and wrapped we are returned that we get out In the action after we in the real is 1st of all has death times the derivative Aug vii with respect to Trevor 5 but now what happens if I have more terms with different powers of aid and coefficients in front of each 1 and but it's still a Eds just Devi by a fiery are This is a linear operation here if if we it tends to be seen more terms with other powers of a nevertheless while we will get will be half times the derivative review with respect the price 1 of these is somebody gives you will you come back and say that it's so so the action half time Devi by define a newbie right you also have it in the complex conjugate star R D but the movie-star five-star bay also what about this time here and times and minus 1 or 2 times fight too young minds to if that causes 2nd derivative that involves a 2nd derivative of B. it's 1 half a 2nd derivative be brands Baer nothin right down because I'm not interested in the things of Bob firm yards right now I'm only interested in things involved the boy on-field fight is also things involving fairly and Fielder important off but for the moment that write down just OK for example if we was vise arid been DVD fire which is proportional defined it was like you it would be of fire square and so forth on but now F is a peculiar thing if only it doesn't of Lagrangian and has not no kinetic terms not derivatives associated word that means the equations of motion for F don't involve derivatives extremely simple the equations of motion just algebraic equations for F without any derivatives and you muzzle solve them eliminate half to do that you write down How cool will in so as involves gaffe involves this coming from the D-2 faded terms and class have star comedy from booster and that you have the full dependents Of the grungy on this so what's called an auxiliary field that's auxiliary because we get rid of it much of auxiliary always means the of the auxiliary Fire Department supporters of major get rid of it I will use the term auxiliary to mean we're going to get rid of it I ate DVD fire process started before I start anus look what is the equation of motion for F well usual equation emotionally involved stuff like derivative with respect extramural muumuu times derivative of our Granzien with respect to boot derivative of efforts respect the expo of our block and then plus minus minus derivative of Grand with respect to equal 0 in this case is very simple book I did doesn't depend on the derivatives rest so this is year Our equation emotion is just a derivative of the Lagrangian with respect the efforts equal to 0 boy is that's a book but right about what was the revoke margin with respect F. Harris D V by D. frying or hot and cost at Star equals 0 another world to immediately and incidentally equation emotions that star you could just get by taking the complex conjugate about various groups derivative of VAT with respect to 5 star super potential class at is equal to 0 Creacy winery should be complex Kroger Gerber here well above trivially solve the equations should just tell us that ass historic is nothing but minus DVD fog plans for complex cottages on order to an EU source AF you could eliminate it and put it in DVD 5 OK whether we CFO reaction we see the reaction here at Star F we see as stars times Devi start before I start was what stock at star Is DVD 5 so this is also going give us DVD flight plans to restart a five-star same kind terms this 1 way or the other soil and the other 1 he will give us exactly the same kind in fact 2 of them have minus signs in 1 of the map plus I my science come from here Minor Sorensen DVD from ring such star Porter a good or if it's all right me as
starters my DVD 5 so both of these this year Aga have negative signs and this will have a positive sign and net results for this it adds up to a potential energy from a to move on June it's a turned a potential energy I want collects not super potential just ordinary potential energy and what is it says ordinary now of little fire up a soup is just f star raft order Josh D V by defied absolute value squared In other words f at star saw some money tells you still example but so an example suppose if I give you that the super potential I'll but areas very busy quartet n not Prime's 580 square and times were big fire square brokers point because matter of pyrophoric are was DVD fight DVD fog is just M serum I gotta keep track of factors of toe today a plot for a factor of 2 0 0 DVD fiery reserve proportional vampires find what about the potential Devi by defy squared persists more fire here small trying DVD squared it just gives us and and squared Tri-Star far better Masters that's a massacre in which women they added through it reclined Gordon Brown Jr. would give recline Gordon particle on maps would give scalar particle maps out so that's it example we worked out West what happened if you were to have they added a fight cubed term meant that should become an fire square again not worry about numerical coefficients defeat if I would be and squared enter the ordinary potential would be V would be score was Jean now not em chief coupling constant Toby G. squared off I squared five-star squared this would correspond door finding diagram in which 2 particles came in and 2 particles worn out fight for the 4th if the whole op shop is that if you're given a super potential Yukon read off from it very quickly with ordinary potential energy of the fielders just the the stupid potential squared our absolute value squares of a very simple process that have about supersymmetric quantum field theory to have to understand a little bit about bra for bar supersymmetry breaking what's plot vertically the ordinary potential energy not the Super potential super potential and ordinary potential a quite different your no potential energy involves the derivative the support Pancho squared but what you've got you got so let plot far-right notice 1st of all that all were always positive where's are here What does not always be positive could be Zero right could 0 became a negative it can't be negative ISO the potential as a function of 580 on on being schematic fire was a complex variable I can draw potential function more complex variable 5 4 a five-star fine but just be schematic it does go have any minimum some twice the minimum is where the vacuum is minimum of the potential energy is the vacuum and field theory minimum value potential energy is the ground-state art and maps to your software theory likes to say that rest or in the back but 1 possibility is that draft beer With the minimum of a potential happens so be exactly the bottom here at V equals 0 the meaning of the Act Super vacuum has no energy appalled the vacuum the energy of a vacuum the potential energy vacuum you're all the comedic energy has to do with time derivatives in space derivatives in the vacuum Moslem out there so the vacuum energy in this case would be exactly 0 what does that imply that implies at the minimum at the place with DVD fight equals 0 has also 0 or another words that at the minimum DVD fire has to be equal to 0 e with with hope while also complex structure white wine or say that for this to be 0 each factory here has to be 0 think the the B 0 editor its of a times on complex conjugate than the thing inside the was also asked 0 OK stop if there is a vacuum with Zero 0 energy it said that DVD 5 is equal to 0 Boone what DVD fires its C after terms in the expansion of the sup field other words it's a component of the Super feels it's a component of the Super four-year-old what it says is but processes that component of the Super few 0 your but it also says the vacuum in supersymmetric wiII be costs for something and not be symmetric some component in a case of angular momentum in the case of a magnetic field always said the vacuum has a component of among 9 of the magnetic field which is not equal to 0 amount breaks a symmetry in the same way if a component in particular the last component of a super field is not equal to 0 that breaks the cemetery white because these different components get mixed up 8 Dewey chopper under a supersymmetric transformation source f In the same way that they components of the angular momentum get mixed up with each other what magnetization get mixed up with each other and our rotation the same thing happens cars the components of a super this statement here is equivalent to saying let me vacuum supersymmetric what seal the possibility the
other possibility is that the minimum of the potential This is not equal to 0 if that's the case then you could make took enclosure was the 1st is that the energy of the vacuum was not going to be 0 vacuum will have some energy all cares about vacuum energy don't people care about ones who worry about gravity you don't worry about gravity vacuum energy is has no implication whatever but you don't worry about gravity vacuum energy is something to worry about it means that the vacuum gravitates vacuum energy use of dangerous thing but if DVD flight is not equal to 0 then that's says that the vacuum has an F terms it has a nonzero component of the Super field roughly speaking pointing some directions superspace then send a super transformation will kind of rotate that it will correspond to supersymmetry breaking of this is not equal to 0 with supersymmetry is broken a vacuum at spontaneous symmetry breaking the theory itself for supersymmetric vacuum simply Paris and energy in it that energy explicitly are were gravitate if this was a rarity theory but don the important thing is if you work out 4 of the details of the equations you'll also find in that case that behaves like a magnetic field F F it's kind of like a component of a magnetic field and has the effect of splitting the massacres of the different particles which rotate into each other on the supersymmetry transformation which are the particles which rotated into to each other on supersymmetry transformation the fermionic and the bombs are ours solid if the main lesson to draw from this is that there he baby series of supersymmetry breaking which is very close in spirit spontaneous symmetry breaking the conventional spontaneous symmetry breaking it does not require the equations to be not supersymmetric it requires the solution of the equations somehow these non symmetric with respect to supersymmetry tree and the result is just like in the magnet the Adam and the magnet collapsed blip levels in the same way we had a lot of the end of the year part of the Adam the magnet would be affirmed the honorable on particle and 2 things which are interchange by the supersymmetry will have their energies from Iran and the bars are that's the implications for missed 1 more fabrication of the vacuum is not supersymmetric if the vacuum is not supersymmetric the simple implication of that just the same way in the vacuum is not rotationally symmetric than a rotation of vacuum gives you something no gives you something which is not the vacuum it gives you a gallstone bars on what happens the vacuum of supersymmetry transformation it is not symmetric under supersymmetry vendors are supersymmetry transformation from a vacuum gives you something new they may wanna guess what that something new is fed riff for a number that supersymmetry transformations interchange bows answer from Iran the vacuum is formally count it as a boss armed state that formerly character as it borrows state but what other vacuum it's a rotation by supersymmetry transformation will change it by handing out me supersymmetry transformation always takes always and or subtract a formula so the result is that whenever supersymmetry is spontaneously broken in this way there is a massless particle and massless particle is a friend beyond stub both on its what happens so the vacuum when you do the supersymmetry transformation the vacuum is symmetric then you don't get anything here were ever vacuum is not symmetric under supersymmetry which means that this is not equal to 0 then when you do a supersymmetry transformation you don't get something new and then new thing is metaphors New York it has and they've Bart sometimes it's of the Goldstone freely on federal Goldstone bars that makes sense because sometimes Korbar broke Steve he nor usually refers to our friend recalled nor the Goldstone Boaz Ala that's the particle generated by doing a small supersymmetry transformation from a vacuum if the vacuum was not symmetric so don't the till consequences are spontaneous supersymmetry breaking your 2 of them 1 is that the vacuum energy is not 0 or the minimum it is not when musical 2 0 0 that's 1 of our back in energy is not equal to 0 and they are the consequences that was a massless fermionic new massless fermionic on expected end as strong as unexpected as are Goldstone Basel on and there for the same reason that the supersymmetry transformation acting on the whole world has to give you a new state and that state His called moves on from the pocket bats a spontaneous supersymmetry breaking in a nutshell 1 more while there are 2 more points of a dubious argues jargon errors of recognize the jargon on the Adam by itself call that a sector of the theory the ad interacts with the from magnet qualifier on magnet another sector of the theory of the magnetic field on the overthrow magnet were exceedingly strong the bill would do something awful Adam Adam would be on recognizable would make spaghetti attitude or Madam looks like worked incredibly strong magnetic field saw the long string he spaghetti looking for right now would be unrecognizable star but the magnetic field is very weak and the Adams quite recognizable and what you would say that that's a situation would be interested in a situation where we magnetic field due to the paramagnet monitors and Sperber burp by analogy the magnetic field of from magnet is very weak the Adams or ordinary Adams and their levels are only slightly Split the reason interested in that situation is because compare the fundamental scale of particle physics string theory grand unified theories or
anything like that which tends to be up there are 16 orders of magnitude larger the particle physics scare the splitting of the Super bronzes hope to be very small talk the super partners are almost the same mass on that scale as ordinary particles that would be an analogous to the magnetic field truly from magnet being very weak and only splitting these particles a little bit of a magnetic field very weak Adams will hardly noticed they would hardly noticed it they would hardly interact with most magnetic fields and in fact 1 of the consequences of this would be that's rather hard by manipulating Adam by manipulating the to rule out to influence a federal magnet weekly coupled some manipulating the Adam would not be likely store up spin waves would not be likely to start up the user of the properties of the from self and then the language reroute the pharaoh magnet would correspond to what's called a hidden sat there at a Hindu sector is back there are on west of this was a very sophisticated Adam you wouldn't even notice the media of a magnetic are magnet which is B pretty kind splitting saw and heard from Magna would be a hidden sector the same light particle physics supersymmetric quantum mechanics are also requires hidden sectors and editions of no objects and no particles in order to break the supersymmetry it's not pretty business Botha to stir contrived business you have to a particles rough day field by the time you finish to have a rather complicated construction and a complicated construction is necessary to Split among the firmly on the bars arms that were released ingredient which does it is often called sector which precipitates the euro researcher breaking over from words took 3rd but Gore with supersymmetry palm yes 1 West Point 1 West Point before we leave supersymmetry altogether From our altogether prefer for tonight gravity has an effect on resource story gravity has an effect on this whole story and that's it's a significant effect on what 1st of all of this has an effect on gravity and 2nd of all gravity has an effect on it it was the effect of a positive vacuum energy if supersymmetry is broke and says that DVD fires equal 2 0 and says that the vacuum energy is 0 What does a nonzero vacuum energy particular positive nonzero vacuum energy due to the world was a tutor work well as a gap it's a cosmological constant because the equations of gravity as a source on the right-hand side of gravity and choruses were accelerated expansion of the universe a rapid if the particle physics scales to your ordinary particle physics Carroll's it would be a very rapid car inflationary rapid acceleration from the universe and it would be quite intolerable if the scales at purity where anything like the scales at appearance standard model or anything or supersymmetric version of it if soft and so it is a bad thing is not a good thing the vacuum energy in the 0 large vacuum energy of theory and the vacuum energy would be quite large death it was what we relied on display at the particles it also throughout artist but the particles this vacuum energy would be huge and were completely destroyed any possibility of being right I won't tell you after factor for a couple fact 1 is the effect of gravity on this equation right here the effect of gravity on this equation right here a head or actually subtract on this other it was . Guerera plunk Mayor right Place ever upside down or more typically me an hour to figure out how our were cars with you but for thank God I think the editor was minus the nor about 3 Iike promised you I wouldn't put numbers this is what I happened to remember our port draw and I think it's clock Mets times he fight that's something the gravity the ask why it's very complicated it's exceedingly complicated your half their bill theories of gravity that supersymmetry that's an extremely complicated story ruined tried but the net result is the gravity heads here the effective our terms could be the shift to prepare sure America in particular if you're very lucky can shifted down to something close enough to 0 that the cosmological constant is small number we know solar gravity is a thing that can conquer the rescue and get rid of vacuum energy as it's very complicated matter tried to drivers and ripped Tom brought bad situation it was rescued by supersymmetric theory what's called supergravity hotspot the other things a little easier door stand but not easy to understand but still easier to understand it has the duel with this on that it's related to the Higgs phenomenon and the Hanks Solana had a property that it took the gallstone bars are and combined it together with the gage Mozart and made gage bows on master so let me just say a few words about back SOsub brings the liberties you to understand on if you have a particle of Spain's Jake force pinned down injured calmly states doesn't have well the answers to Jaipur Lisbon states to J. plus 1 so for example if the spin of a particle was 1 of photon has been 1 any laws on has been 1 then it has 3 states right to J. was 1 3 states and so forth storm depending on the spread of the particle now a full-time
only has 2 spin states and that's connected with the fact that massless so let's let's say some things about per particle masses and spins so for bodies suppose it I told you that pick our what's what's but suppose the book master let's suppose a photon rest and it'll only has who's been states mainly spill along its direction emotions as been Mecca point along the direction of motion or of the spin vector pointing opposite direction emotion yes they want to buy only 2 states yes are archery under young menu automata something inconsistent about this us recite if the photon has amassed Yucatan rents transformer or equivalently rewarding keep up with the phone consular has no momentum bought a spend Lorenzo transforming it doesn't change the fact that its spending so let's take this spring stayed here and low rents transformed so were moving up along with that fuck Tonawanda has any momentum but has a spin and now Leyritz transform it monopoly in this direction he won't we made with me a photon who spins Is not along its direction emotion as we brought the rest and then transformed it in some other direction so that for if the vote count is messy it has perhaps old read spins has perhaps been taxes trucks in opposite to its axis end of the 3rd been state also on on the other hand if the on is massive restless you can't bring it arrest you can't bring it arrest you can't do this operation will you could do with a rotating higher state of photon without bringing it arrests and all actors simultaneously rotate momentum and the of spin was initially along the axis of the emotions will stay that way the upshot is massless particles massless photon for example can have and does have only the 2 of Spain's states all along the taxes and are perfect How does the gage bows on how the gage bows on of electroweak theory get another component of spit it would be component of spin off along the direction emotions where spin along the direction of motion was 0 plus wanted minus 1 and knows been along the c-axis or altogether where does that extra component of the spring come from Passover the movie full or full time by Susie bows on Aug bows on could be massive wears a come from an economist from the Goldstone bars on the gallstone laws on together with the tool polarization states the tool spin states of the massless Ian W. combined together and make enough states to be the master of Zia W which requires 3 states the same exact thing happens when you combine to particles from a supersymmetric theory the took particles are 1st of all the massless gravity no sorry mess 1st young math was never get the massless Goldstein massless Goldstein always course from our idea the massless Goldstein Spiegel has to spin states like electrons exactly like electrons and the restless Goldstein open you have it's been all along the axis of motions are opposite the axis of motion was up article which is the supersymmetric particle partner although we grab will you talk about graphic arms with you all know they exist over half to exist at a gravitational theory are so what's a spillover Gravatai don't spin to right the spin-off of its partner is not a half spring particle its a spin three-year particle spin to in spend 3 have formal it's also massed because it's a partner of the granite pardons so we have to kind of messed with there will be an early on so if talk kind of mess was friendly on a distinct and they different what is a gravity know where charitable along this axis can have Spain 3 hands along axis or minus history have Long rapturous but if a one-man still you would also have backed 2 0 other spin states spin 1 hand and minus this 1 half time after have the rest of the full sprint multiplex have perhaps been might History of minus 1 half plus 1 here really where where can and those of the 2 components come from picking come from Goldstein or so the Goldstein combines together with a Gravatai in exactly the same pattern as the Goldstone bows can combined together with the gage goes on to make a massive object that believed the Buick and be a case of course nobody knows of mysterious right but if it is right there will be on massive spin camps particles from we never scene and elementary particle spin 3 hair so it will be a mess messes spent 3 years ago but it will be His horrid to produce in a laboratory as it is to produce a grab part will be no easier which means you not Tennessee Of the match best the supersymmetry I'm sure it's more than you thought you want nor Barrett for its it's more of war Barrett about a half nor Barbara because requires through which are my contract for Stamford yes Tarramba Ron were absolutely finished with the mathematics of supersymmetry now welcome back some physics of Red Road Map a mathematics sure that's a good rose on foot the then those is it grand unification also is a somewhat mathematical subject not as bad not nearly as abstract mathematics is a little bit of group theory knew we sticker Our said Mary break and there were achieved subjects where Cheney subject the something much easier born spare Harvey as you 5 as your 5 is a simple theory to understand
juror now with this story about CP violation Fermilab since the conflict however harbor experiments and people were less enthusiastic about the work but saw archives reporting where workers ranch what at last if the Hummer pretty good living betting against anything their it's very rarely we be wrong of course postcard you really be wrong but how right so have gone the Standard Model issues based on group theory best you 3 cross escudo cross you want SU 3 is the group Bob Court of quirks as you too is the weak interactions and a new 1 is closely related electromagnetic interactions in a way that I'll be a little more precise about today West Western parliament has yet to reconstitute cost you warned is a grope grope that consists are separate transformations 3 things too things one-third but people have wondered whether a hole structured could be embedded in some summer growth which is Morris symmetric and more simple the rest of 3 Grosser Street to cross you want as you 3 courses cost you 1 fits in very nicely into the group rescue 5 so it it was asked whether numerous people asked a small number people answered whether it was possible that there might be some big good growth in which a large number of particles or collect structure which a larger number of particles would fit together into a single multiplex remember that there are the SUV 3 consist of a quirks BSU multiple its while courts have some amassed Udo but they also have semester 3 yeah you're also lap on slept arms you but they don't have to 3 the question is might be fit together in something more symmetric and bigger natural can they you fired the reason is because just 3 courses best 5 is the simplest grope smallest group that contains astute three-course through cross you want as a sub sorrow Craig Ito explained to you a little bit about what that means and the easiest way to explain it In terms of the generators the groups S U 5 it is just the group of special unitary fiber fiber makers should use this remind you what what special means award unitary means your unitary means unitary means that bagger you a cyclical 1 and special means that the determinant of you 4 1 5 is absolute value is determined determinant of your product of the Eigen values determined review physical 1 in general the unitary group cannot determine which is at which is a features heatedly I later a the special set it is a sector which has determined he recalled 1 this can be translated think the generators were nor generators mean it means that small deviate group elements which small deviations away from the identity as to the identity element this the No. 1 half beef small deviations away from the identity element small in fear possible transformations can be written in the form of 1 of identity plus ii times of small number I times 1 of the generators grow generators of the group corresponds to a different directions about which different the independent of directions of transformation that you could do with the a case of angular momentum will be free taxis in the case of a S U 5 some sort of independence generators comedy generators or there for harmony independent the newly independent generators or off off we will work that out minute theater turns out to be a quit talk about before and so you characterize the group by the generators and the commutation relations among generators but before we do that You'll literary character all of the group that of the group elements translate ain't over her mission character of GE GE it is equal to g Bakker veteran abstract group statement but also or concrete statement 5 by 5 In my matrices where Muslim our specialized 5 by 5 matrices but everything I say also true for Bayern matrices a group S 5 the generators 5 by 5 matrices but off 5 by 5 matrices and generators 1st of all have to be permission secondly we determined condition is the condition that the the trace of GE is equal to 0 trace permission makers use that is analogous to the Paoli matrices rescued to the Cali matrices rescued our mission and they have no trace the tries so the Polly matrices to be a special case now but APEC what's it would
encounter many such independence matrices are 5 5 linearly independent well if I by 5 matrices their her mission that means Our off badly on diagonal elements are real and the off diagonal elements is real we don't know Rio gone bad elements ofthe bag over moves are complex in general but when you reflect them about the axis should they just complex conjugate maps the character of our mission matrix so the question is how many parameters are their only real parameters real independent real parameters or there's matrix this dialog With B total number of them by an extra and squared Cook said it looks like this constraints C is equal to see dagger however that was a good cuts the number of components in half but not really because a complex number has a real and imaginary part so this is still independent components 2 independent real numbers and these stood together are simply too independent real numbers just as it looks so the number of independent components of a square Our mission Matrix Partners and square but then we have to subtract 1 for the trace condition trace condition some of the bag elements set up 0 so the answer is direct in squared minus 1 generators are the group you when was just check that prefer 1 case that we know for S chilled and squared minus 1 would be to square mile swim would be 3 and they would be the 3 hourly matrices 3 components Oliver angular momentum would be example 3 component spin OK so the cases you 5 your 24 independent 25 miners 124 independent generators of the grow that's a lot but when fortunately when I craft deal with most of them the question is which subset of Beirut which subset of them correspond the generators not as you free S U 2 0 new 1 hour erupts serves not hard to figure out you could provide the 5 by 5 maker shoes into it rows and columns Fulham here and free from here all them here 3 of them here the door here offer a suitable if you are up here in the quarters the generators of S you 2 would generators arrest you are 3 generators Robert the Paoli matrices in the context of Spain the Nepali matrices are usually called sit in the context of internal symmetries often called How how 1 count too How 3 so right now he shall free the draft I 1 minus 1 0 0 1 1 1 0 0 tower 2 0 minus are 0 0 those over 3 policymakers these major stake in this corner matrices notice that they are there already 1st they are mission and it put Zero everywhere else these are the generators of S future these algebra these commutation relations of them everything about them is for properties of a palace themselves and so among the fire by 5 makers to use generators subset which just live in this corner Roma here are generators Our the group suture to what was done here all right down 8 of them they usually land has nothing to do with the cosmological constant direct 8 of them 3 bite 3 3 by 3 her mission trace was matrices both the generators rescue break it's also resource Baker Suter lives up and he and S U 3 and he I never S U 2 and yes to 3 major by themselves Our trace West is 1 additional generator which commutes with all of these which commuter laws ban which describes do you want properties of elementary particles you want particle and that a diagonal matrix which has 0 it commutes you too because it's proportional to the identity and he outlets call it puts worker caught her off Rob we could call at minus 1 minus 1 dozen minus 1 of Plus went matter body just changes sign of it that would just tourists just at a convention with people minus 1 plus what are plus 1 and he both to be unit make bricks in the tool dimensional Saab Burma substructure here associated with 2 sources unit matrix with minor this case are put in here for a reason I have to do with old conventions and that in here you put the whole thing has to be traced Lewis and I wanna put something he at which commutes with all the S U 3 generators all 2 generators it has to be proportional to the unit matrix in here needed to be I needed to be if this is 1 of the trace of this 1 I want two-thirds two-thirds and two-thirds 0 everywhere results this generate as anemic
its quote y the generator of a S U 5 years which distinguishes the S U 2 blocks from you 3 it has different values and the escudo block a dozen years Reebok yes to block it has values minus 1 and yes to 3 block it has value to I've chosen two-thirds here was a convention that I put minus 1 he occur but anything here as long as these 2 with the same but in order to make it have 0 tried similar words to make that some of the elements B 0 I had put two-thirds these are the generators of the group a report that back label the states particles label the state of quirks and wept times to be exact a label estates were also pigs bars arms and shown now I will tell you How is structure works how connected with the articles on their fruit just billing astute 3 more about SUQ I might put here for better port I would say the U 3 matrices unitary 3 matrices act on a column vector of quarks whether the column that the colored quarks red yellow and green or whatever we call mix them up among themselves what about be to block the ESU to block year I could push for example neutrino on electron neutrino electron or mix by astute tool as firemen here and so the question is what particles show I identified with the basic 5 play with the basic 5 dimensional column right here that these exist you 5 transformations act on price but the into that Roh will answer it by just some guessing and somber of some some educated guesses OK on a brief all we do it let's try down the whole collection of fairly yarns there in the Standard Model fall collection of them now I authorize the whole collection biggest economy in family has become 3 families the electron neutrino are down family arm want a neutrino Our charmed strange family and West Ham with balls powers the other quirks actually just focus on what family now the electron neutrino quark Obama or family which I pull them how many there are and see how we might fit them into 0 representations of arrest you 5 now why want to representations or what would be the implications of that agreement as you fired remember the back this symmetry grope also has other complications during DG bows answer go with the symmetry group for example the yes you 3 were the Gables arms for the yesterday remove begin the Guam backed by a you want associated with a generators of S U 3 What about the ISU Toby both have to do with the W plus W minus Men of Zeal or some combination of zeal for Cardiff pop star so there are going to be no gage votes on new gage goes on 24 of them up till now we had 2 0 0 plus 8 can there be 14 mortgage borrowers on the 14 mortgage Moslems would be associated with these corners are here and they will have implications will be new interactions no forces associated with who kinds of particles and that's what we want have price or track down off the particles now before I do star what I have something else as you know freelance come in left-handed and right-handed pipes the left-handed pair Meaghan's other ones which interact weakly with the weak interaction only left-handed and have yes you to the right in the of writing in the from Iran's no weak interactions only left-handed from arms weak interactions on the other hand the color actions are there among for exports left-handed right so this is an odd sort of peculiar structure Todd B S cost you want is usually identified as astute to cross you 1 of left-handed particles not write him particles that the relationship between a left-handed particles and right him particles the forward what 1 left there was right here but there's another way to think about you would think of it as particle an entire article The in that article of a right here particle is itself left here it is not a left-handed reader and that article of a left electron Is there is a right he indeed possible hand in this changes were new role from particle prep article that means you could you could label all of the particles as left-handed if you like among electrons for example Tuesday the independent electron states far left hand that electronic left positron end do it by particles the and that particle fear that particle of the left-hander lecture argued is our right here and in the positron nearby particle Of being
left-handed positron is a right-handed electron so you could either say that independent objects are particles and by particles but you could also just I insist on labeling Wallaby independent objects as a left-handed and particles just concentrate on the left objects label although objects as left-handed or the impact particles of left-handed particles that's another way to work to describe all of the answer the Standard Model we can all be thought of as left-handed we had that particles of left-handed particles so let's all go well focused on a left-handed particles and let's see how many of them there are was just add up everything was a left-handed neutrino left-handed neutrino Nataline on was left left-handed just what of neutrinos a command of beta decay a left-handed Mr. left-hander electron that bars Mustafa calling on left-handed left-handed draw
ended the art quirk a mail order Oracle Valley quarterback B and bogged down quarks now I have written I have the obviously not written all particles down a written down only 5 years 5 2 5 by a white right there misfired will see a mom look that all want the freeway of IDU court no you quote you quote retrieval electron down bar down bogged down by 1 of his three-year was him for 3 colors recall are so this is 1 subset and broken up this way will become clearer OK the next a subset of the remaining ones over here are Supreme must also our to repair are bounded down Barry Bob Baffert at bar standard-bearer pop pop pop but but up Bar Harbor bar bar parent EU classed as he might electrode positron among the electron top quark bank worker or here is a electron here's the positron it is not believed to certainly not the standard marble the neutrino is only by particle so there is not a separate and that particles from the train all the electrons to win that particles here the 3 down quarks era there and that particles here of a free up quirks here antiparticle and here is the past brawl that the fact that I wrote them in this way judges chose to write Ms. selects the rough I'm only here and I hope can only be a 1 2 3 4 5 6 7 8 9 10 so altogether there are 15 part of its 15 particles are replicated times we electron neutrino system gets replicated as new new 1 neutrino was electron neutrino are risk is replicated 3 times all of these get replicated 3 times but let's not worry about the replication where that comes from nobody knows where it comes from far but no reason show you wiII teII him on why I chose particular pattern here it's pretty clear that what goes up in here if I want to write a column vector now of fairly arms it's pretty clear that what goes up in here should not have color right why because SU 3 doesn't act on the 1st 2 our the 1st 2 slots as you too lax as you 3 not 1st 2 slots here show me things which have no collar but which mixed up on you too erodes which makes up on movies as you were resistant to transformations Powell so I can that be beat well neutrino electron mixed up on the morrow left-handed vitriol and left electron get mixed up bias you to and they don't have color see only thing you could borrow a year would be neutrino electron the a fact that put train on top an electron to some extent that's convention so resort of neutrino on top electron the need was just because that's the way it usually red what broke down here then he and I want to put quarks but those quirks have SU free but no OSU tool which of the quarks have S U 3 but Norwest future members of the right here quirks left courts and weak interactions due to the right here quark stop I have always the right-handed quarks here I was all particles In time as you go left in the particles or left pet articles the group here which don't have a weak interaction which is that particles Our an RBI worry if died quarks New Whiskey you bar people these are the ones that do not have any S U 2 properties they are and that particles of the right-handed quirks the quirks are not the ones that interact beta decay in the weak interactions they are neutral or they don't transform Honda as you told Nagel by particles so these other guys here if you library label everything is left-handed these other people here which don't transform Monday as you to which of these or what part in this slot OK so now I will tell you how figure out 1 of the gage is going to to be the photon photon couples store electric charge the electric charge must be 1 of the generators of this is you 5 brother was the whole thing would make set off BSU
5 quantum numbers are supposed to be of all of the quantum numbers of the electroweak QCD color theory or was at me that means electric charge color quantum numbers and the things which have to do with Ian W. electric charge has to be 1 of the generators Of course you but all the generators of S U 5 entrees it was a medium that we use that means in a given multiplex the sole means of electric charge will be given multiple at half the Arab 0 Aceh statement back generators of S you 5 reveals that's exactly the same thing saying no Botswana minus 1 in favor of the more bizarre multiplex the love of how 302 spin for members of the Opel down the songs of the 2 spins components a spin it up 0 same thing for us you 5 if you have a multiple of S U 5 particles transforms and as you 5 any given generator the describes a quantum number the songs of numbers must get up 0 so whatever we put here it has to be such that electric charges all aid up 2 0 with a 0 electric charge this has electric charge minus 1 of some here must be a plus 1 which on these particles has charge which adds up plus 1 passes for d quarks have charge minus a 3rd in ID quirks have charge plus occurred saw 0 0 also quantify charges Iran minus 1 and now if I put we can't b quarks here this altogether has charged plus 1 plus 1 plus 1 plus 1 plus a 3rd plus a 3rd plus a 3rd and the sons of all of them equal 0 of our work but the you works that will and die you quarks they have charged 2 thirds forget this year they have charged 2 thirds and the charges would not have been as you are so it's about a group trips comments from be ultimately it comes from Riyadh to trace to trace listeners of the generators Of the group that were trying the label particles body while labeling them by generators S you 5 in the summer of elements of us U 5 with a 4 0 of some of these charges 0 romp that picks out b quarks audit by d quarks and by day courts because those are the ones that do not have as you took or numbers don't get mixed up by bias astute it really is that way and this is a part of really every boy don't put the rest of the particles the rest of the particles can them stop the next question is is there my Clark some exports to back this will fill out the remaining 10 particles in another representation of S U 5 not a fine dimensional representation but guess what but they never saw representation theory is attend dimensional representation theory is the representation the 10 dimensional representation has exactly the right properties the be the remainder of these particles here this is either a fantastic accident bar or it was something deeper than I don't think it's a accident remaining particles he exactly fill out and the regional representation Brostrom saw combat nor should have artworks game a a new law not be these particles do not get mixed with these group transformation if that shareholders attack each other but not by by not body out do interactive each other but there is no DARK sorts but the question the let's take the gloom 1 for example by 1 of these particles Kim immutable 1 become 1 of the other ones they can knock you may gone become more of these black a deep bar can minute gone which is absorbed by EU Corker example so it the generators take the generators which are the same as Riyadh as the emissions matrix elements for the belongs here they take 1 quarter when I think these please don't take this however that doesn't mean at same thing he said thank all of the generators of us you find these up among themselves makes these up among themselves do not mix these movies but that's simply means that nor about Babesiidae interact with side you have to eat made and absorb so you perhaps before the Group of Five over here interact with the Group of Ten over here by exchange a big boats on a prank get there also the Higgs boards on gets into it the mix and for more
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