Anonymous at Wed, 16 Oct 2024 07:21:35 UTC No. 16434037

>>16434032
If you mean GUTs, then all gauge symmetries become one. That symmetry is the one that gets broke to produce the standard model symmetries. Yes, all particles interact with each other, but this is nothing new. All particles in the standard model already interact with one another at the electroweak scale since their hypercharges are non-zero.

Anonymous at Wed, 16 Oct 2024 07:29:39 UTC No. 16434043

>>16434037
i mean all particles already interact through gravity, but my point is if there are new interactions and basically if conventional conservation laws, besides the univeral ones like energy or angular momentum, stay valid.
Like, does conservation of electric charge still remains?
The way i see this worded is that the coupling constants tend to converge to the same value.. but this says nothing about newer interactions

Anonymous at Wed, 16 Oct 2024 07:41:45 UTC No. 16434052

>>16434043
>if there are new interactions
yes. Your gauge group changes, so there are. Particularly there must be new gauge bosons since those correspond to the gauge group, which is now enlarged.
>conventional conservation laws, besides the univeral ones like energy or angular momentum, stay valid
what you probably mean is charge conservation laws. Since the SM group is necessarily a subgroup of a GUT group, all charges remain conserved.

What is not conserved however are so-called “accidental symmetries”. Baryon number violation is the most prominent example as Georgi-Glashow’s theory predicts proton decay. But these accidental symmetries aren’t sacred. Baryon and lepton number symmetries are there because the strong force doesn’t interact with the latter. Since both leptons and quarks become the same thing in GUTs it is easy to see that these numbers may not be conserved anymore.

Anonymous at Wed, 16 Oct 2024 08:35:11 UTC No. 16434077

>>16434052
>accidental symmetries”
Accidental how?
I dont know the technical terminology, but you mean its like a conservation law that only sticks within a limited set of interactions, and not a universal law?

Anonymous at Wed, 16 Oct 2024 08:39:22 UTC No. 16434080

>>16434077
I hope you're not eatin' dat chicken

Anonymous at Wed, 16 Oct 2024 08:40:23 UTC No. 16434081

HELL

Anonymous at Wed, 16 Oct 2024 08:40:48 UTC No. 16434082

>>16434080
what chicken

Anonymous at Wed, 16 Oct 2024 08:42:55 UTC No. 16434084

>>16434082
You know which chiken

Anonymous at Wed, 16 Oct 2024 08:47:48 UTC No. 16434085

You have to farm chicken properly, or face hell.

Anonymous at Wed, 16 Oct 2024 08:50:00 UTC No. 16434087

>>16434052
Huh? This sounds very abstract and has no material basis.

So it would be helpful to classify these as theoretical to help students understand the difference in reality.

Sure mathematically it Can be changed to create some symmetry but for all intents and purposes you are just playing around with physical parameters abstractly. None of this is actually proven.

It's Intellectually dishonest to make absolute and declarative statements pertaining to theoretical physics.

This is all hypothetical anon.

Gravity is a major problem in unification because it's force is unknown. Can electromagnetic force and gravity interact? Black holes say yes but come on we can't actually prove that

Anonymous at Wed, 16 Oct 2024 08:52:31 UTC No. 16434089

>>16434084
no i dont

Anonymous at Wed, 16 Oct 2024 08:56:08 UTC No. 16434093

>>16434087
>Can electromagnetic force and gravity interact? Black holes say yes but come on we can't actually prove that
Isnt gravity supposed to interact with everything any way?
Why is it that black holes can allegedly break Baryon or Lepton conservation, some speculation about unification conditions at the black hole? (very high energies as particles fall into the hole).

Anonymous at Wed, 16 Oct 2024 09:50:30 UTC No. 16434135

>>16434093
No gravity only interacts with mass. Which is why newton's physics work so well with rockets. We can calculate the exit velocity of a rocket using his equations.

But say like the infinitely small or electromagnetic forces. It's a bit uncertain how gravity interacts with these forces because it's beyond humans ability to observe or measure.

So it is speculative in nature. This is why theoretical physics doesn't focus on experimentation. But the solid principles of mathematics.

Which is a little shaky on its foundation because there is no way to prove your hypothesis or mathematical measurement.

Pay attention to this word.

MATERIALLY.

So any symmetry found is questionable because the material components of that measurement have no observeable basis. Other than speculation

To answer your question about black holes reference above words.

The big bang and black holes violate bayron conservation. Both are unobservable and unmeasurable in reality

Made up by some retarded guy in a wheelchair Stephen Hawkins.

Anonymous at Wed, 16 Oct 2024 10:05:51 UTC No. 16434142

>>16434135
What is the argument that black holes violate lepton and baryon conservation?
New interactions that are only possible at high energies and the black hole conditions or early universe provide those energies?

Anonymous at Wed, 16 Oct 2024 16:50:18 UTC No. 16434652

>>16434077
It has nothing to do with the actual underlying symmetries of the model. Baryon and lepton number conservation only happen because quarks and leptons are in different representations of the SU(2) group. If they were in an another set of representations, then these wouldn't hold. This tells us nothing about the underlying symmetry group, hence accidental.
>>16434087
>Huh? This sounds very abstract and has no material basis.
Engineers still struggling to understand that math is used to described reality. Sad.
>Gravity is a major problem in unification
GUTs don't include gravity and only concern themselves with spin 1 fields.

Anonymous at Wed, 16 Oct 2024 16:53:29 UTC No. 16434657

>>16434032
Complete bullshit math wank which will all be abandoned at the first sign of new experimental data which gives actual reasons

Anonymous at Wed, 16 Oct 2024 18:34:44 UTC No. 16434885

>>16434052
>Since the SM group is necessarily a subgroup of a GUT group, all charges remain conserved.
This is too glib. The GUT group is a gauge group and doesn't involve corresponding conserved charges in any simple way. Electric charge conservation must correspond to some global U(1) symmetry of the matter fields Higgsing the gauge symmetry.

Anonymous at Wed, 16 Oct 2024 19:05:08 UTC No. 16434960

>>16434885
>and doesn't involve corresponding conserved charges in any simple way
never said it was simple. But it works the same way as say the electric charge-weak isospin-hypercharge relation in electroweak theory. There are conserved Noether currents in the original theory. Once it undergoes symmetry breaking, the charges corresponding to the residual symmetry (with the appropriate gauge bosons that didn’t gain mass) are linear combinations of charges in the original theory. This is a basic consequence of the residual symmetry being a subgroup of the original one. The adjoint representation decomposes in a perfectly predictable way, even if working out the details may be messy.
>Electric charge conservation must correspond to some global U(1) symmetry of the matter fields Higgsing the gauge symmetry.
Two comments. First, gauge symmetries are local. Not sure what global symmetries have to do with this. Secondly, not sure what electric charges and the (electroweak) Higgs mechanism has to do with GUTs. The main goal of GUTs is to have these representations included, but GUTs themselves only ever concern themselves with breaking down to the Standard Model group. The electric charge is a conserved current in an already broken Standard Model group. For example, in Georgi-Glashow we have
SU(5)->SU(3)xSU(2)xU(1)->U(1)
where the second arrow is the well known SM Higgs mechanism.

Anonymous at Wed, 16 Oct 2024 19:07:00 UTC No. 16434968

>>16434960
*obviously meant SU(3)xSU(2)xU(1)->SU(3)xU(1), where it should also be noted that the two U(1)’s are only isomorphic but not equal.

Anonymous at Wed, 16 Oct 2024 19:24:34 UTC No. 16434998

>>16434960
>Not sure what global symmetries have to do with this
I didn't think you would understand, that's why I commented. Consider a simpler theory. SU(N) Yang-Mills. Are there U(1) subgroups of SU(N)? Yes, plenty. Are there any conserved charges in the actual theory corresponding to them? No. All physical states are in the trivial representation of SU(N) since it is a gauge group.

Now consider adding one flavor of quark to the theory. There is now a U(1) global symmetry transforming the quark fields while leaving the gauge fields untouched and there are physical states (baryons) with non-zero values of charge. Whatever the mechanism is for breaking SO(10) or whatever down to SU(3)xSU(2)xU(1) may be, the resulting U(1) charge conservation is related to a global U(1) symmetry of the underlying matter fields.

Anonymous at Wed, 16 Oct 2024 19:32:18 UTC No. 16435011

>>16434657
I think anon here is right. Once the proof comes. Everything will change instantly. No reason to argue what we can't prove.

Anonymous at Wed, 16 Oct 2024 19:45:50 UTC No. 16435046

1/2
>>16434998
Again, I have to point out several things which I do not understand with your reasoning.
>Are there U(1) subgroups of SU(N)? Yes, plenty. Are there any conserved charges in the actual theory corresponding to them? No.
Let me preface this with the following. Charges are representations of the group. You’re asking whether an SU(N) theory contains U(1) representations. The obvious answer is no. Why would it? It contains SU(N) representations. What you’re confusing is charges and charge-carriers ie gauge bosons aka the adjoint representation, which is uniquely determined by the group. U(1) representations obviously don’t manifest as SU(N) representations because that’s not the whole group. Now, when we break the group via a Higgs representation, then if the residual symmetry is U(1), then the gluons would become n^2-2 heavy bosons and a single photon. I see absolutely no issue here as what we observe is the whole group. Moreover, SU(N) is a simple group, so U(1) isn’t a normal subgroup and there are in fact none such subgroups. I mention normal subgroups because that’s where you could argue that the charge carriers manifest as separate entities since one can quotient out the adjoint rep in a meaningful way while preserving group structure. And this is what we precisely see with the Standard Model group, which is semisimple rather than simple.

Let me put forth another argument. SO(3) is a subgroup of the Lorentz group. It clearly has its own representations (spherical harmonics). Do we care about those in special relativity? No, not at all, because those representations aren’t Lorentz-covariant. Similarly, U(1) representations aren’t SU(N) covariant.
>Now consider adding one flavor of quark to the theory
Flavor is a completely separate symmetry. It’s global and not local. We have no idea where it comes from. Nothing to do with gauge theory.
>There is now a U(1) global symmetry
Yeah, because you introduced it yourself. And?

Anonymous at Wed, 16 Oct 2024 19:51:33 UTC No. 16435057

>>16435046
2/2
>while leaving the gauge fields untouched
what’s that supposed to mean? Gauge fields are unique. You can’t have flavors of gauge bosons. They emerge from the adjoint action of the Lie group on its representations. It’s an extremely restrictive structure.
>the resulting U(1) charge conservation is related to a global U(1) symmetry of the underlying matter fields
no fucking shit, because that’s the exact same symmetry you had assumed at the start which has nothing to do with gauge theory.
>All physical states are in the trivial representation of SU(N) since it is a gauge group.
This is the dumbest sentence in the entire post. You know what we call the trivial representation? The vacuum. Quarks can’t be in the trivial representation because they fucking interact. Quarks are in the fundamental representation. Georgi-Glashow includes additional representations such as the antisymmetric rank 2 tensor of fermions or an adjoint Higgs representation in addition to the fundamental one.

Anonymous at Wed, 16 Oct 2024 20:27:25 UTC No. 16435127

>>16435046
>Yeah, because you introduced it yourself. And?
And it remains a symmetry of the actual theory. There are actual states in the quantum theory that transform non-trivially under the U(1) global symmetry. There are no states that transform under the local SU(N) symmetry.

Let's consider another model. The original SU(2) Georgi-Glashow model, where an adjoint Higgs breaks SU(2) down to U(1). Unlike the previous case, there is no global U(1) flavor symmetry of the Higgs field, and similarly there are no charged states in the actual theory, despite having an unbroken U(1) sector. That is my point. Charge conservation has to do with global symmetry.

Anonymous at Wed, 16 Oct 2024 20:30:36 UTC No. 16435131

>>16435057
>This is the dumbest sentence in the entire post.
>You know what we call the trivial representation?
Glueballs are non trivial states in the theory. They do not transform under SU(N). Please be respectful. You simply are not understanding what I am saying because you have not thought much about the actual states of the quantum theory.

Anonymous at Wed, 16 Oct 2024 20:31:33 UTC No. 16435134

>>16435011
Precisely. Stop circlejerking citations on immaterial schizo topologies and start collecting some fucking data from the real world.

Anonymous at Wed, 16 Oct 2024 20:35:15 UTC No. 16435139

>>16435046
I'll recommend this paper to you. arXiv:1810.05338. Just ignore the stuff about quantum gravity. The bulk of the paper is a review of a nonperturbative understanding of global and gauge symmetries.

Anonymous at Wed, 16 Oct 2024 20:46:20 UTC No. 16435162

>>16435134
>>16435011
>>16434657
NTA
i dont understand the math of what they're talking about.
A truly intelligent person would say "I don't know enough to have an opinion".
You are all coping with your retardation and saying "obviously this is absurd (because I can't understand it)"
Kill yourselves, you subhuman subniggers

Anonymous at Wed, 16 Oct 2024 20:46:33 UTC No. 16435163

>>16435127
>And it remains a symmetry of the actual theory
Cool. And? What does this have to do with GUTs?
>There are no states that transform under the local SU(N) symmetry
SU(3): quarks (fundamental representation) and gluons (the adjoint representation
SU(2): every left-handed fermion of the standard model (fundamental representation), the Higgs (fundamental representation) and the W/Z bosons (the adjoint representation)
>The original SU(2) Georgi-Glashow model, where an adjoint Higgs breaks SU(2) down to U(1).
That’s not the original model. The original one is SU(5) and for a very good reason. It’s the smallest group that includes the Standard Model. If you mean “the simplest toy model for the Higgs mechanism”, then sure.
>Unlike the previous case, there is no global U(1) flavor symmetry of the Higgs field
The Higgs doesn’t have flavor. There is only one Higgs representation in the Standard Model. The flavor group of the standard model, U(3), includes three completely separate copies of first generation representations.
>Charge conservation has to do with global symmetry.
Please pick literally any book on field theory and go to the chapter on gauge theory. See how the gauge-covariant derivative is constructed. It literally requires locality as a prerequisite. This can be derived both algebraically by explicitly doing the transformations or geometrically via Wilson loop.

Both global and local symmetries have corresponding conservation laws by Noether’s theorem. However, only local symmetries induce conserved CURRENTS and not just charges. The simplest example of that is Poincare symmetry, which is global in special relativity but local in general relativity. We have energy, momentum and angular momentum conservation in both, but only in general relativity does LOCAL Poincare symmetry give rise to the stress-energy tensor obtained via functional differentiation of the action wrt the metric.

In summary, you’re a Dunning-Kruger retard.

Anonymous at Wed, 16 Oct 2024 20:51:19 UTC No. 16435179

>>16435163
Look up Elitzur's theorem. Reread my posts. Understand that you misunderstood everything I was saying.

Anonymous at Wed, 16 Oct 2024 20:52:41 UTC No. 16435186

>>16435131
>Glueballs are non trivial states in the theory
Has nothing to do with what I said. Glueballs are composite particles. You don’t have to go this far. Quarks aren’t in the trivial representation of the SU(3), because, guess what, they interact with gluons. Leptons are in the trivial rep of SU(3), so they don’t. Not rocket science.
>You simply are not understanding what I am saying because you have not thought much about the actual states of the quantum theory.
My graduate research was on GUTs. Bitch, fucking please.
>>16435139
I don’t want to go through yet another paper on string theory when gauge theory is a basic topic in QFT that has been known since Weyl. It’s covered in every field theory book. No need for fancy “modern” papers.

Anonymous at Wed, 16 Oct 2024 20:54:33 UTC No. 16435193

>>16435179
Oh, I remember you. You used the exact same reference a while back. Ok, Elitzur’s theorem. So? Can you use your own words instead of appealing to authority?

Anonymous at Wed, 16 Oct 2024 21:14:23 UTC No. 16435222

>>16435193
>>16435186
>My graduate research was on GUTs. Bitch, fucking please.
Great, I figured as much. But you are not understanding what I am saying. Physical states in the Hilbert space of the quantum theory are in a trivial representation of the gauge group. This is not controversial. I am sure you understand this if I make absolutely clear that is what I am talking about. This is why I say pure Yang-Mills (no quarks) only has states in the trivial representation. It has glueball states in the Hilbert space but they have no SU(N) charges.

On a related note sure you can write charge conservation expressions with covariant derivatives from the classical equations of motion, but they are only are manifested in the theory as Ward identities in correlation functions. There are no states in non-trivial representations of the gauge group, and so there is no (non-trivial) notion of the gauge group generators commuting with the Hamiltonian, which is what you would want for conservation laws in the quantum theory.

Now electric charge conservation involves physical states with non-zero values of electric charge, so how is this consistent with Elitzur's theorem and so on? What I am arguing is that the symmetry associated to charge conservation is better understood as a global flavor symmetry. This is why I brought up the toy model SU(2) Georgi-Glashow model as an example to better illustrate the distinction I was making. Because there is no global symmetry of the Higgs field distinct from the SU(2) gauge symmetry, and there are no charged states in the theory, even though there is an unbroken U(1) subgroup.

Anonymous at Wed, 16 Oct 2024 21:45:50 UTC No. 16435269

>>16435222
I am not understanding what you're saying because you've spent this entire thread going into non-sequiturs and misusing basic terms. I have pointed out all of them and I will do so once again below. Just a warning. I have better things to do than to argue with Dunning-Kruger crackpots. I genuinely believed that you had valid criticisms about my explanation of GUTs, but this entire conversation has gone on a complete unrelated tangent. So this is my last (You).
>Physical states in the Hilbert space of the quantum theory
You mean on-shell states? Observables? For someone who tries to "correct" me you sure can't use precise language to drive your point home.
>It has glueball states in the Hilbert space but they have no SU(N) charges.
Glueballs are composite particles that are gauge-invariant. Of course they are trivial. What's next, you're going to tell me how baryons are also in the trivial representation? Every observable needs to be gauge-invariant ie in the trivial representation. So? Every observable also needs to be Lorentz invariant. You're telling me there is no Hilbert space with [math]|l m\rangle[/math] kets?
>There are no states in non-trivial representations of the gauge group
Ok, I'm talking to a schizo who denies the Standard Model. There are no quarks. There are no weak doublets above the electroweak scale. It's all made up.
>There are no states in non-trivial representations of the gauge group, and so there is no (non-trivial) notion of the gauge group generators commuting with the Hamiltonian
The generators are in the fucking adjoint representation. They literally cannot be trivial. You, sir, are a certified crackpot who doesn't know the basics.
>Now electric charge...
basically that whole paragraph boils down to "I don't believe in the Higgs mechanism and I have my own pet explanation that I believe in." What any of this has to do with GUTs is beyond me. Adios.

Anonymous at Wed, 16 Oct 2024 21:52:33 UTC No. 16435278

>>16435269
>So? Every observable also needs to be Lorentz invariant. You're telling me there is no Hilbert space with |lm⟩ kets?
This is something fundamental you seem to be misunderstanding. Gauge symmetry is not like global Lorentz symmetry. There are states in a Lorentz invariant theory that transform non-trivially under Lorentz symmetry, the |lm> kets and so on. There are no states in a gauge theory that transform non-trivially under the gauge symmetry.

Anonymous at Wed, 16 Oct 2024 21:56:48 UTC No. 16435285

>>16435269
>The generators are in the fucking adjoint representation. They literally cannot be trivial.
Just to be clear, I'll respond to this too. The generators annihilate all physical states in the Hilbert space. This is the sense in which they are trivial.

Anonymous at Wed, 16 Oct 2024 22:05:06 UTC No. 16435306

>I'll use my own made-up definition
>according my definition, they are trivial

Anonymous at Thu, 17 Oct 2024 13:14:14 UTC No. 16436221

>>16435269
I'll try one more reply

>I have better things to do than to argue with Dunning-Kruger crackpots.
Considering you are someone who doesn't understand basic things in a field very closely related to your own, I think you should hesitate calling other people Dunning-Kruger. If you want to learn about these things read textbooks like Greensite's "Introduction to the Confinement Problem", and for how the Hilbert space works in gauge theories read Henneaux and Teitelboim.

>For someone who tries to "correct" me you sure can't use precise language to drive your point home.
It is quite precise to call the states in a Hilbert space "states." It baffles me how you could misunderstand this since I was very clear. As I said before you probably are only used to thinking about Feynman diagrams and Lagrangians and not the actual Hilbert space.

>There are no quarks. There are no weak doublets above the electroweak scale. It's all made up.
There are indeed no quarks as states in the Hilbert space. You can think of this as an aspect of confinement in gauge theories, but it is a rather weak notion of confinement that is true in both confining and Higgs phases. Some people call this property of gauge theories "color confinement" to distinguish it from a notion of confinement which is not present in the Higgs phase.

>The generators are in the fucking adjoint representation. They literally cannot be trivial.
I said this in the above post, but they annihilate all the states in the Hilbert space, so they trivially commute with the Hamiltonian. This is the only sense in which you have charge conservation. All charges vanish for all times. A non-trivial notion of conservation would have non-trivial symmetry generators that act on the Hilbert space and still commute with the Hamiltonian. Maybe you are not used to thinking about this, but that does not mean I am making up language or being unclear.

Anonymous at Fri, 18 Oct 2024 16:43:40 UTC No. 16438196

>>16434032
idk

Anonymous at Fri, 18 Oct 2024 16:51:17 UTC No. 16438208

>>16434652
>quarks and leptons are in different representations of the SU(2) group
What do you mean by this? Im not by any means an expert on this but i thought these elementary particles were representations of the Lorentz group (which itself can be represented by two SU(2) groups) and that both quarks and electrons were spin 1/2 particles and essentially identical as far as you can model them as independent particles with no interactions, which isnt realistic for quarks.
I mean, wasnt that the work done by Wigner and Dirac and a few others, of finding all possible representations of the lorentz group, each one representing a possible type of elementary particle?
So i dont understand what you mean by quarks and electrons being different representations of SU(2). I mean i literally dont understand it, not saying you are wrong

Anonymous at Fri, 18 Oct 2024 17:02:38 UTC No. 16438237

>>16438208
I meant the SU(2) component of the SU(2)xU(1) electroweak group, not the Lorentz group. Obviously both are fermions.

Anonymous at Sat, 19 Oct 2024 17:48:01 UTC No. 16440042

>>16434032
idk

Anonymous at Sat, 19 Oct 2024 18:18:00 UTC No. 16440096

>>16438237
>I meant the SU(2) component of the SU(2)xU(1) electroweak group
gotcha, but i still dont understand what it means. All i ever undewrstood about group representations in QM was that elementary particles were representations of the lorentz group.
The way i understood it is that any representation of an elementary particle is going to be an object that can be acted upon by a representation of the lorentz group, which will change its "state", so in a way all there is a 1-to-1 relation between elements of the lorentz group and particle states (for a given particle, like an electron).
This doesnt say much about interactions (or anything), just about free particles.
So what does it mean to say that an electron or quark is in a different representation of the electroweak group?