Well, the collapse is an effective description, projecting away the part irrelevant for the subsequent experiments. Once one measures (and absorption counts as a measurement), relativistic invariance is broken anyway...vanhees71 said:
The Haag-Kastler framework is more permissive in this respect. since it is not bound to the vacuum sector. In the Wightman framework you need to describe electron-electron scattering by keeping some far away positrons around (in the AQFT parlance a 'charge behind the moon'), which is a bit ugly.vanhees71 said:
But in electroweak theory, a physical state can have a non-zero SU(2) charge, am I right? I don't fully understand why physical states can have a non-zero SU(2) charge, but cannot have a non-zero SU(3) (color) charge; where does the difference come from, exactly?vanhees71 said:
Isn't it entirely up to if the model has asymptotic freedom or not? Quarks and SU(3) is not enough, you need to specify representation and number of states for the sign of the beta functionDemystifier said:
I wish I had accessvanhees71 said:
So if I'm wrong in this thread, I believe I'm wrong in a non-trivial and interesting way.vanhees71 said:
yes.vanhees71 said:
One problem with your analogies is that they don't show that the first is not realized in QCD.Demystifier said:
A purely theoretical question (not realized in actual nature). What if we extend the Standard Model by adding couplings between Higgs and gluons, analogous to the couplings between Higgs and weak gauge bosons? In that case gluons become massive due to the Higgs mechanism and gauge invariance becomes spontaneously broken. In that theory colored states could be realized, right? And yet the theory is still gauge invariant at a more fundamental level.vanhees71 said:
So how is one W-boson, or one electron, weak-SU(2) gauge invariant?vanhees71 said:
That's misleading. An S-matrix element is a probability amplitude. As such, it can only be measured in an ensemble. A single measurement never gives you the S-matrix element. On the other hand, a single measurement detects a single electron or a single W-boson. It's not clear in what sense it's gauge-invariant under weak-SU(2) gauge transformations.vanhees71 said:
Fine, but it still doesn't explain how one electron state is gauge invariant. It must be so, but I don't see how to prove that it indeed is.vanhees71 said:
I guess the answer to my question is something like this. Physical states are those which are annihilated by the BRST charge. A gauge transformation of a physical state, say one-electron state, adds a zero-norm state to the initial state, so it represents the same physical state. That looks fine.vanhees71 said:
The deconfined phase of QCD is a many-particle state, hence the phrase ''The one-quark state in the deconfined phase of QCD'' is meaningless.Demystifier said:
That's a misconception from the 1980ies. Today it's clear that the "QGP" which can be produced in heavy-ion collisions is far from being a thermal-equilibrium ideal gas of massless quarks and gluons. One rather has a strongly coupled liquid, and still there's a kind of confinement. How to really understand this state is far from being clearly resolved.Demystifier said:
Not necessarily. For example, if a many-particle state is a simple tensor product of one-particle pure states, then we can talk of well defined one-particle pure states.A. Neumaier said:
A different phase is a different sector of states. The Hilbert space of the deconfined phase is disjoint with the Hilbert space of the vacuum sector. There is no decomposition of the states of the deconfined phase into well defined one-particle pure states.Demystifier said:
Instead of taking about phases of QCD, which apparently nobody understand very well, let us talk about phases of water. Ice is a "confined" phase, steam is a "deconfined" phase. I think we can talk about single molecules within steam.A. Neumaier said:
Yes. But this is because here particle number is conserved and the molecules are not quasiparticles. As a consequence, the phase transition doesn't generate a different sector unless the thermodynamic limit is taken, where the particle structure disappears.Demystifier said:
1. Since you point out that molecules are not quasiparticles, are you suggesting that some would-be analogous objects in QCD are quasiparticles? Which ones?A. Neumaier said:
The quasiparticle structure in nonrelativistic QFTs is analogous to the sector structure of relativistic theories, obtained by redefining the vacuum of the Fock space. The renormalization in relativistic QFT does the same. There the unphysical, bare particles are the Fock particles, whereas the physical, renormalized particles are what would be called quasiparticles in a nonrelativistic setting.Demystifier said:
Because the thermodynamic limit (where the volume and the number of particles become infinite) changes the structure of the ##C^*##-algebra of observables (particle number is no longer an observable) and hence the state space. Without the thermodynamic limit one has no discontinuous phase diagrams, hence no rigorous phase transitions.Demystifier said:
I see. But what if we look at all this from the the point of view of lattice QCD? The lattice is assumed to be finite, so there is no thermodynamic limit in a rigorous sense. In a regime in which it describes confinement, the bare quarks are unphysical particles, while the dressed states, like mesons and nucleons, are physical quasiparticles. But even on a finite lattice one can study phase transitions in a non-rigorous phenomenological sense. So in this sense I would expect that, at high energies/temperatures, the bare quarks become physical particles, very much like electrons in Fermi gas. Or at least, that the quarks only wear a "swimming suit", so that the physical states don't differ much from bare quarks, very much like the quasiparticles in Fermi liquids. Does it make sense to you?A. Neumaier said:
Electrons in a Fermi gas are quasiparticles, not particles. The vacuum structure of them is different from that of the bare vacuum, and the quasiparticle Fock space is disjoint from the bare particle Fock space.Demystifier said:
Can you support it by a reference?A. Neumaier said:
Biss, H., Sobirey, L., Luick, N., Bohlen, M., Kinnunen, J. J., Bruun, G. M., ... & Moritz, H. (2022). Excitation spectrum and superfluid gap of an ultracold Fermi gas. Physical Review Letters, 128(10), 100401.Demystifier said: