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But the charge color is well defined. What happens after cooling down of the soup, if the initial hot soup has non-zero charge color?PeroK said:Quark number is not that well-defined.
But the charge color is well defined. What happens after cooling down of the soup, if the initial hot soup has non-zero charge color?PeroK said:Quark number is not that well-defined.
If you could create a colour-charged soup, then QCD would be broken!Demystifier said:But the charge color is well defined. What happens after cooling down of the soup, if the initial hot soup has non-zero charge color?
Consider the following experiment. (It's a gedanken experiment, but should be possible in principle.) Consider a big container filled with a hot color neutral soup of quark-gluon plasma. Now insert a wall in the container which divides the container into two compartments, labeled A and B. The plasma in A does not need to be exactly color neutral, and similarly for B, but together they are exactly neutral. Now separate A and B at a large spatial distance from each other. Finally, after the separation, cool down A at a low temperature, so that confinement can take place. Given that A was not initially color neutral, what happens in A after the cooling?vanhees71 said:You start with color-neutral Pb nuclei (gauge-invariant bound states of quarks and gluons if you wish) and all you can create is a soup of "quarks and gluons" that all together are color neutral too.
It doesn't make sense. QCD is asymptotically free so nothing prevents colour-charged soup at high temperatures.PeroK said:If you could create a colour-charged soup, then QCD would be broken!
You cannot create a non-zero color-charged soup, because you can't have a color-charged object to begin with. Asymptotic freedom only implies that at huge temperatures and/or densities the quarks and gluons move quasi freely within the soup (aka a QGP) but as a whole the soup is color-neutral.Demystifier said:But the charge color is well defined. What happens after cooling down of the soup, if the initial hot soup has non-zero charge color?
Yes you can, see the experiment in #38.vanhees71 said:You cannot create a non-zero color-charged soup, because you can't have a color-charged object to begin with.
That experiment reminds me of the various attempts to subvert the UP. Either it would subvert QCD. Or, when you look at the fine detail, QCD would somehow ensure that both halves were colour neutral.Demystifier said:Yes you can, see the experiment in #38.
Then where do these intermediate states come from, if not from the theory?PeroK said:My understanding is that these states are not part of the theory. Not that they exist but decay too fast for current experiments. This is why I made reference to you as a "Bohmian" early. If you take QCD as a realist theory, where quarks exist with hidden classical trajectories, then there must be free quarks for at least a short time. But, if you take QCD as an abstract mathematical theory, then these intermediate states are not part of the theory.
Fine, this reduces the problem to a more elementary problem of interpretation of short living resonances. Are they real or not? Note that they are not virtual states in Feynman diagrams, so according to general postulates of QM they should be real and measurable in principle. They are not measurable by current technology, but could be measurable with future technology. In fact, there is no well defined limit how short living a particle must be to call it "resonance", the borderline between particle and resonance is not sharp.vanhees71 said:I'd rather say they exist only within the theory and are not referring to anything observable. Even in non-confining theories like QED the "transient states" of interacting fields have no physical interpretation as observables.
PeroK said:That experiment reminds me of the various attempts to subvert the UP. Either it would subvert QCD. Or, when you look at the fine detail, QCD would somehow ensure that both halves were colour neutral.
I don't think that color neutrality is such a fundamental principle as you think it is. I don't see any theoretical argument for that. Given that QCD is asymptotically free, I don't see why should both halves of hot quark-gluon plasma be color neutral.vanhees71 said:I doubt that this gedanken experiment can be done in the real world. It's of course a complicated not yet fully solved problem, how "fragmentation" works, i.e., that you always end up with color-neutral states.
This would require adding energy to the system which would cause the creation of additional quarks/antiquarks to make both sides color neutral. It's no different from the thought experiment of trying to pull apart a meson or baryon to obtain free quarks: you end up with additional quarks being created so you get multiple mesons or baryons instead of free quarks.Demystifier said:Now separate A and B at a large spatial distance from each other
Why? The quark gluon plasma is in the high-temperature asymptotically free phase, i.e. the particles are almost free.PeterDonis said:This would require adding energy to the system which would cause the creation of additional quarks/antiquarks to make both sides color neutral.
Resonances are real as "bumps" in a cross section. What you meausure are cross sections describing the scattering of asymptotic free "in-states" to asymptotic free "out-states". It's described by a complex pole in the corresponding Green's function.Demystifier said:Fine, this reduces the problem to a more elementary problem of interpretation of short living resonances. Are they real or not? Note that they are not virtual states in Feynman diagrams, so according to general postulates of QM they should be real and measurable in principle. They are not measurable by current technology, but could be measurable with future technology. In fact, there is no well defined limit how short living a particle must be to call it "resonance", the borderline between particle and resonance is not sharp.
The same can be said for long-living (quasi-stable) particles, there is no sharp difference between resonances and long-living particles. Indeed, I think that's how top quark was discovered, as a short living resonance.vanhees71 said:Resonances are real as "bumps" in a cross section. What you meausure are cross sections describing the scattering of asymptotic free "in-states" to asymptotic free "out-states". It's described by a complex pole in the corresponding Green's function.
Because once you start pulling A and B apart, the space between them is not hot quark gluon plasma, it's vacuum, and your reasoning based on everything being at high temperature and asymptotically free breaks down. (In fact, even putting a wall between A and B is enough for that reasoning to break down if the wall is not itself made of hot quark gluon plasma.)Demystifier said:Why?
If that argument was right, then thermodynamics (not only of quark gluon plasma, but also of ordinary gases) would work only for systems with infinite volume, because if the volume is finite then there is an outside space so not everything is at that temperature. And yet, we know that thermodynamics works for finite systems too. In particular, quark-gluon plasma does not need to have infinite volume. Hence your argument does not convince me.PeterDonis said:Because once you start pulling A and B apart, the space between them is not hot quark gluon plasma, it's vacuum, and your reasoning based on everything being at high temperature and asymptotically free breaks down.
Not at all. Thermodynamics works just fine for finite systems provided you take into account what happens at their boundaries. All I am doing is pointing out what must happen at the boundaries of the quark gluon plasmas A and B once you start separating them.Demystifier said:If that argument was right, then thermodynamics (not only of quark gluon plasma, but also of ordinary gases) would work only for systems with infinite volume, because if the volume is finite then there is an outside space so not everything is at that temperature.
I didn't say it did. I only pointed out the obvious fact that once you separate two quark-gluon plasmas, the space between is not quark-gluon plasma, so you are no longer talking about internal asymptotically free motions of quarks within a single quark-gluon plasma, you are talking about separating two quark-gluon plasmas, which requires adding energy to them, which in turn creates additional quarks to make each one color neutral individually, where before you separated them you just had one quark-gluon plasma which only needed to be color neutral overall.Demystifier said:quark-gluon plasma does not need to have infinite volume
That's the part I don't understand. Why the separation requires adding energy?PeterDonis said:you are talking about separating two quark-gluon plasmas, which requires adding energy to them
Fair enough, but then how about my proof in #26? Would you say that the energy of such states would not only be large, but actually infinite? But it can't be infinite because the lattice is finite. This can be seen heuristically by considering two quarks: the potential energy between them increases with distance, but the distance cannot be infinite on the finite lattice.PeterDonis said:Similarly, a single free quark at rest, which is what the OP was describing, is not part of a hot quark gluon plasma, so it's irrelevant to talk about the properties of a hot quark gluon plasma in that context.
Because that's how the strong interaction works once you get beyond distances of about the size of an atomic nucleus: increasing the distance between strongly interacting particles requires adding energy because of the strong attractive force between them. This is the flip side of asymptotic freedom: at very short distance scales, the strong interaction becomes weaker (asymptotic freedom), but at longer distance scales, the strong interaction becomes stronger.Demystifier said:Why the separation requires adding energy?
Heuristically, I would expect that it would because I would expect the spherical shape to be the lowest energy shape, as it is for attractive forces generally in hydrostatic equilibrium (at least if we assume negligible rotation).Demystifier said:Suppose that initially the plasma is spherical. If you want to reshape it without breaking it into two parts, does it also require energy?
Your proof there is based on the idea that if the free theory contains color charged states, the interacting theory must also contain such states. But the fact that a state exists mathematically in the Hilbert space does not guarantee that it is physically realizable.Demystifier said:how about my proof in #26
No. The Hilbert space of QCD only contains colorless states. Single quarks live in a nonphysical Krein space with indefinite inner product. The Hilbert space of QCD is a subspace of this Krein space with positive definite inner product. This subspace only contains colorless states.Demystifier said:The state he imagines (single quark state with zero momentum) is a legitimate state in the QCD Hilbert space.
at high temperature is not the same as at high energies. Free quarks at high temperature are very complex ensembles of composite quasiparticles in a high temperature bath.Demystifier said:It does not say that color-charged particles don't exist at all. It only says that they can't be observed at small energies.
Not only that, but bound states also don't exist. Neither is there a dynamics, because the theory is defined as a Euclidean QFT, not a Lorrentzian one! Lattice QCD is therefore very nonphysical. Its physical predictions require limits that invalidate all your arguments, since the limiting single quark states are not well-defined!Demystifier said:Let me consider QCD on the lattice, so that the theory is mathematically well defined by having a finite number of degrees of freedom. This guarantees that there are no UV and IR divergences and that the Haag's theorem does not apply.
How does this follow?Demystifier said:Since QCD is asymptotically free, if follows that color charged states is possible for a soup of quarks at a very large temperature.
This is nonsense. A single water molecule at low temperature is completely stable. It cannot crystallize for want of other water molecules...Demystifier said:Can we have an isolated water molecule at low temperature? One will say no, because water molecules like to "confine" into a solid crystal. But it really means that an isolated water molecule is unstable, not that it's impossible.
In the bath there would be one extra quark to neutralize the lone antiquark! But the whole argument makes no sense because quark number is not well-defined, so you cannot count...Demystifier said:uppose that the soup contains 1 billion quarks and 1 billion plus 1 anti-quarks. After cooling down, you get 1 billion mesons plus 1 anti-quark extra. What happens with the extra anti-quark?
Yes, and in this sense we can talk about the fate of an isolated quark…. But, as is often the case with natural language descriptions of quantum behavior, we are using the words in a way that is completely at odds with a layman’s understanding of what they mean.Demystifier said:Due to interactions it is not a Hamiltonian eigenstate, but it is a state. Hence, in principle, it can be an initial state and it is legitimate to ask how such initial state would evolve with time.
Not really. Single quark states have negative squared norm, hence no probability interpretation. Thus one cannot interpret them in any physical way.Nugatory said:in this sense we can talk about the fate of an isolated quark….
Yes, which is why describing their forward evolution in time doesn’t correspond at all to the lay understanding of forward evolutionA. Neumaier said:Thus one cannot interpret them in any physical way.
That's interesting. Can you give a reference for more details?A. Neumaier said:The Hilbert space of QCD only contains colorless states. Single quarks live in a nonphysical Krein space with indefinite inner product. The Hilbert space of QCD is a subspace of this Krein space with positive definite inner product. This subspace only contains colorless states.
That's what's investigated in heavy-ion collisions. There is pretty much evidence for the fact that at the highest energies of collisions of heavy nuclei (such as at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory or at the Large Hadron Collider at CERN) a socalled quark-gluon plasma is formed.PeterDonis said:Heuristically, I would expect that it would because I would expect the spherical shape to be the lowest energy shape, as it is for attractive forces generally in hydrostatic equilibrium (at least if we assume negligible rotation).
we already discussed this here in a long thread about QCD. It is standard material, like in QED in the Gupta-Bleuler formalism.Demystifier said:That's interesting. Can you give a reference for more details?
Very relevant paper, but it actually claims less than you said.A. Neumaier said:we already discussed this here in a long thread about QCD. It is standard material, like in QED in the Gupta-Bleuler formalism.
Kugo, T., & Ojima, I. (1979). Local covariant operator formalism of non-abelian gauge theories and quark confinement problem. Progress of Theoretical Physics Supplement, 66, 1-130.
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