Abstract
We report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge-fixing method and which show an improved agreement with the continuum results. By relating the Gribov confinement scenario to the center vortex picture of confinement, it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector, a vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. The effective potential of the Polyakov loop is evaluated from the zero-temperature variational solution. For pure Yang–Mills theory, the deconfinement phase transition is found to be second order for SU(2) and first order for SU(3), in agreement with the lattice results. The corresponding critical temperatures are found to be 275 MeV and 280 MeV, respectively. When quarks are included, the deconfinement transition turns into a crossover. From the dual and chiral quark condensate, one finds pseudocritical temperatures of 198 MeV and 170 MeV, respectively, for the deconfinement and chiral transition.
Highlights
One of the most challenging problems in particle physics is the understanding of the phase diagram of strongly interacting matter
A vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences
I have presented some recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge
Summary
One of the most challenging problems in particle physics is the understanding of the phase diagram of strongly interacting matter. There are semiphenomenological approaches assuming a massive gluon propagator [14] or the Gribov–Zwanziger action [15]; see [16] In this talk, I will review some recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge both at zero and at finite temperatures; for earlier reviews, see [17, 18]. I will show by means of lattice calculations that the so-called Coulomb string tension is linked not to the temporal but to the spatial string tension In this context, I will demonstrate that the Gribov–Zwanziger confinement scenario is related to the Advances in High Energy Physics center vortex picture of confinement. I will give some outlook on future research within the Hamiltonian approach
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