Tell me everything about quarks

[Anonymous No.15176853]

Why do quarks exist? Are there equations that predict their existence? The Dirac equations predicts electrons and positrons, does something like that exist for quarks?

[Anonymous No.15176858]

>>15176853
There is currently no empirical evidence that quarks exist and the model is purely hypothetical

[Anonymous No.15176860]

>>15176858
What is the model anyway?
Any equations predict their existence?
They are supposed to be spin 1/2, do they follow Dirac's equation?

[Anonymous No.15176861]

>>15176853
There's no explanation for anything in the universe. It's magic.

[Anonymous No.15176862]

>>15176858
oh bs
https://www.slac.stanford.edu/pubs/slacpubs/0250/slac-pub-0369.pdf

[Jealous No.15176863]

There is a well known question in QFT about finding exact solutions to the anharmonic Phi^4 field. One might call that the main question about how QFT works. One other hand, there is a more fundamental question which asks, "Why do we have the particle we have not some other ones? Why six quarks and six leptons but not seven of one and five of the other, with 11 zerberts too?" I call that the fundamental question of quantum field theory and I think I solved it. The spectrum of lattice vibrations in my cosmological model (pic) is exactly the spectrum of particles in the standard model and that is very good because a QFT is often constructed by taking the limit of vibrating lattice as the lattice spacing goes to zero.

[Jealous No.15176864]

>>15176863
>is exactly the spectrum of particles in the standard model

[Jealous No.15176869]

Sixty-Six Theses: Next Steps and the Way Forward in the Modified Cosmological Model
https://vixra.org/abs/2206.0152
The purpose is to review and lay out a plan for future inquiry pertaining to the modified cosmological model (MCM) and its overarching research program. The material is modularized as a catalog of open questions that seem likely to support productive research work. The main focus is quantum theory but the material spans a breadth of physics and mathematics. Cosmology is heavily weighted and some Millennium Prize problems are included. A comprehensive introduction contains a survey of falsifiable MCM predictions and associated experimental results. Listed problems include original ideas deserving further study as well as investigations of others' work when it may be germane. A longstanding and important conceptual hurdle in the approach to MCM quantum gravity is resolved. A new elliptic curve application is presented. With several exceptions, the presentation is high-level and qualitative. Formal analyses are mostly relegated to the future work which is the topic of this book. Sufficient technical context is given that third parties might independently undertake the suggested work units.

[Jealous No.15176871]

http://gg762.net/d0cs/papers/Sixty-Six_Theses__v2-20220726.pdf

[Jealous No.15176872]

>>15176858
The Nobel prize awarded to Gross, Politzer, and Wilczek for the discovery of asymptotic freedom pertains to the direct empirical evidence for quarks.

[Anonymous No.15176882]

>>15176863
Bro the question you say you solved is much more elevated than the one i asked (im the OP). Instead of wondering why some theoretical particles exist and not others, i just want to know how quarks are even a thing, theoretically.

[Jealous No.15176887]

>>15176882
Oh, my bad.

[Anonymous No.15176895]

>>15176887
Do Quarks obey Dirac's equation or some alternative variation of it? They are spin 1/2 after all.

[Jealous No.15176902]

>>15176895
I'm not sure. It is thought that quarks only exist in groups with other quarks (due to confinement) and that would suggest something more than the Dirac equation is going on because electrons (or leptons) can exist on their own.

[Anonymous No.15176904]

>>15176882
>>15176887
I mean, im not even considering why quarks are either real or not. As a simpler analogy, consider the prediction of positrons by the Dirac equation. Some might have believed at the time such prediction meant nothing, others that it could be a real thing. But at least there was a mathematical construct, i want to know if something like that exists for Quarks

[Anonymous No.15176909]

>>15176902
Something else can go on and also the Quark field may follow some equations.
For instance electrons follow Klein-Gordon equation, but they also follow the Dirac equation.

[Jealous No.15176912]

>>15176904
Negative time kind of popped up in the same way that the positron popped up. Kind of in the way the neutrino popped up too. I think we're really beyond the point now where the implication of a working theory is only a mathematical construction. If the theory works, itis reasonable to assume that its facets describe reality.

[Anonymous No.15176913]

>>15176902
The reason im asking is that i read that fundamental particles are all irreducible representations of the Poincare group, i also heard that quarks are referred to as fundamental particles, so do they correspond to some Poincare group representation or are they something else completely?
You say quarks cant exist alone, does suggest something not like a fundamental particle or that multiple quarks together "are fundamental"

[Jealous No.15176916]

>>15176912
I think only real electrons follow KG. KG doesn't allow off-shell electrons whose existence are fairly certain by now, unless I am mistaken.

[Anonymous No.15176923]

>>15176853
There weren't equations. There were similarities between heavier particles and lighter ones and a group structure was derived for u, d, s. From there it was speculated there was a fourth quark named charm to complete the pairs (u, d), (c, s). Then there were speculations of additional pairs (generations) and b was later discovered, then t followed in 1995. There were analyses done for reasoning why there wouldn't be a 4th generation. With the 3 generations, that's where you get the pyramid for baryons and other structure for mesons.

[Anonymous No.15176931]

>>15176923

[Jealous No.15176934]

>>15176913
I would have to go back and check my notes to remember exactly what a representation of a group is, friend. I feel like the representations of the Poincare group are rotations, translations, and boosts but, like I said, I don't have the group theory jargon fresh in my mind right now. Also, there's probably something about the distinction between a field and its excitation that is relevant but which also escapes me at the moment.

[Anonymous No.15176938]

>>15176923
Mesons

[Jealous No.15176941]

>>15176934
>rotations, translations, and boosts
These might be the group generators, actually.

[Anonymous No.15176952]

>>15176923
>There were similarities between heavier particles and lighter ones and a group structure was derived for u, d, s.
You mean this came from experiments?

[Anonymous No.15176954]

>>15176913
Quarks have asymptotic freedom so are "free" at high enough energies. They are fundamental, but cannot exist alone at low energies. The amount of energy it takes to separate two quarks goes into the building energy (larger at greater distance) until there is enough to create a quark anti-quark pair to reduce the distance between them to lead to overall lower energy state

[Anonymous No.15176960]

>>15176954
Binding* energy

[Anonymous No.15176974]

>>15176952
Yes, they identified particles with similar properties. Consider the [math] \sigma^- \sigma^0 \sigma^+ [/math] particles. They looked fundamental and so did a large number of others. The distance between them (charge) could be explained by a different composition of quarks but they looked like 3 of same or similar mass particles with different charges. The [math] \sigma_b [/math] are the same just heavier and can be explained by a b quark instead.

[Anonymous No.15176982]

>>15176974
[math] \Sigma [/math] not [math] \sigma [/math]

[Anonymous No.15176990]

>>15176952
>>15176974
A telling sign that they weren't fundamental was the [math] \Delta^{++} [/math] as it has charge 2 which is unexpected and not seen as normal. Jokes on them though as now we have fundamental particles with fractional charges of e (2/3 and - 1/3)

[Jealous No.15176993]

Yes, let us give due consideration to [math]\Sigma^pm[/math]. This will be a worthwhile endeavor.

[Jealous No.15176996]

Yes, let us give due consideration to [math]\Sigma^{\pm}[/math]. This will be a worthwhile endeavor.

[Anonymous No.15177011]

>>15176934
The gist of it is that when one does an actual calculation on some field that represents a given particle, one can also do transformations of that field by acting on it with operators. The operators are representations of the poincare group, in the sense that you can multiply two operators ad you get another operator and the structure is just like that of the Poincare group.
And that any possible state of the particle can be defined as "operators acting on some initial state". The operators change the initial state and give you another state with different speed, momentum, position, etc.
In this sense, you can describe the particle not by its state but by the operators that "create" the state by acting on some initial state.
Sort of the idea that you can describe the orientation of a 3D body by giving the rotation matrix that puts it into an orientation.
For fundamental particles theres more structure than this, because they have quantum numbers that arent just spin, momentum, position, and so on. These are universal properties, but specific particles will have more structure like having electric charge.

But the poincare group has many representations, so you can have many different "mathematical objects" that still behave like a group that follows the group laws of the Poincare group.
In the jargon it is said that "particles are representations of Poincare group" but to me is more natural to say "particle transformation form a group, poincare group, and each representation is a fundamental particle".
So that you can predict all fundamental particles just by figuring out what the representations of this group is.

[Anonymous No.15177024]

>>15177011
How do you enumerate all representations of a group? Or is it just the irreducible representations of a group that are the particles? If that's true, is there a relationship between count of generators and count of irreducible representations?

[Jealous No.15177033]

>>15177011
>And that any possible state of the particle can be defined as "operators acting on some initial state"
Yes, one obtains an arbitrary momentum state by applying a boost to a k=0 state, etc. It's just the group theory words that I'm not remembering. I am good on the physics.

>>15177024
>How do you enumerate all representations of a group?
Maybe with a Young tableaux?

[Anonymous No.15177038]

>>15177033
Right sorry been a while since seeing Young tableau

[Anonymous No.15177043]

>>15176872
>words words words
Not evidence

[Anonymous No.15177046]

>>15177011
Therefore, if one was to do calculations on a "quark field" on paper or a computer one has to actually write down the field as some type of vector, spinor or generalized tensor field. One does this with electrons and positrons, they come from the QED lagrangian, one can write down the "euler lagrange" equations and solve them, etc. I want to know if this is possible for quarks too.
>>15177024
I dont know how to enumerate all the representations of the Poncare group BUT i will tell you that for the SU(2) group (which isnt the poincare group i know) one can find infinite countable representations
https://en.wikipedia.org/wiki/Representation_theory_of_SU(2)
These just look like matrix groups, you have 2x2 matrix, 3x3, 4x4 matrix, until infinity. They are all SU(2) but are different realizations of it, and you give each an number to identify them.
What i heard is that Poincare group is just like this but more complicated, and that it may behave as two SU(2) groups multiplied or something, or maybe SU(2)xSU(2) is the Lorentz group, i dont remember, but in any case you can write it down or at least name it by giving some set of identification numbers.
Both the poincare, lorentz and SU(2) groups also have continuous representations where the index number isnt countable and where you cant represent them as simple matrix groups of some dimension.

[Anonymous No.15177047]

>>15177033
Does that imply that the number of dimensions gives rise to the number of generators from boosts and rotations and that the number of particles depends on the number of dimensions? Seems strange that more particles could exist in 4D than 3D

[Anonymous No.15177057]

>>15177024
>Or is it just the irreducible representations of a group that are the particles
Its only the irreducible representations. What this statement actually means is that the particle can be transformed from "any state to any other state" without forbidden regions. Or if we talk about operators that form groups, that you can get any element of the poincare group by multiplying other elements.
What it means is that your set of group elements cant be some sort of subgroup like rotations, so you could then have particles that do nothing but rotate and have no translations, no boosts, no nothing, just rotation. So no representations are allowed that are subgroups, that what i believe irreducible means, though the definition is more abstract sometimes

[Jealous No.15177061]

>>15177047
I'd have to check my notes on that. My own program, being more geometric in nature than algebraic, wasn't really a good venue for group theory. By that I mean that I drew the picture of what I was thinking about and then I noticed that it was like the standard model in its permutations. An average undergraduate set to get a B in his abstract algebra class probably knows more about group theory than I do, even while I may be as interested in the underlying structures as Galois himself was.

[Anonymous No.15177306]

>>15176860
Electrons don't even follow Dirac's equation. One of the states has more energy in experiments than is predicted by Dirac's model. Chromodynamics and Quantum Electrodynamics is a scam btw.

[Anonymous No.15177313]

>>15177306
I accept it as an approximation of electrons. I want to know if anything like it exists for quarks.
Another form of saying this is if theres some lagrangian that explains the strong force. It may be than in this system the interactions are so strong that it isn't realistic to talk about single fields so one must consider all the fields together always.

[Anonymous No.15177314]

>>15176853
In standard model QFT , yeah there's a quark field and gluon field, the theory is called QCD , quantum chromodynamics.

It's analogous to QED , quantum electrodynamics, which has a Dirac field and the EM field.

[Anonymous No.15177348]

>>15177314
https://en.m.wikipedia.org/wiki/Quantum_chromodynamics
I see it now. A lagrangian with the quark fields and the gluon fields. I suppose the interaction is so strong it isn't representative to talk about independent quarks.
Looks also that if the coupling g were set to zero, one would have free quarks that would be just like electrons.

[Anonymous No.15177786]

>>15176869
Why do you constantly spam this in other people's threads ?

[Anonymous No.15178266]

>>15177786
Because he's a faggot

[Anonymous No.15178981]

>>15176853
they rhyme with pork