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Register a new userHamiltonian approach to Yang-Mills theory in Coulomb gauge - revisited
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I briefly review results obtained within the variational Hamiltonian approach to Yang-Mills theory in Coulomb gauge and confront them with recent lattice data. The variational approach is extended to non-Gaussian wave functionals including three- and four-gluon kernels in the exponential of the vacuum wave functional and used to calculate the three-gluon vertex. A new functional renormalization group flow equation for Hamiltonian Yang--Mills theory in Coulomb gauge is solved for the gluon and ghost propagator under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
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I review results recently obtained within the Hamiltonian approach to Yang-Mills theory in Coulomb gauge. In particular, I will present results for the ghost and gluon propagators and compare these with recent lattice data. Furthermore, I will give an interpretation of the inverse of the ghost form factor as the dielectric function of the Yang-Mills vacuum. Our ansatz for the vacuum wave functional will be checked by means of functional renormalization group flow equations, which are solved for the gluon energy and the ghost form factor. Finally, we calculate the Wilson loop for the vacuum wave functional obtained from the variational approach, using a Dyson equation.
I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribovs confinement scenario is realized in this gauge. For this purpose I will discuss in detail the emergence of the horizon condition and the Coulomb string tension. I will show that both are induced by center vortex gauge field configurations, which establish the connection between Gribovs confinement scenario and the center vortex picture of confinement. I will then extend the Hamiltonian approach to QCD in Coulomb gauge to finite temperatures, first by the usual grand canonical ensemble and second by the compactification of a spatial dimension. I will present results for the pressure, energy density and interaction measure as well as for the Polyakov loop.
I 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 $275 , mathrm{MeV}$ and $280 , mathrm{MeV}$, respectively. When quarks are included, the deconfinement transition turns into a cross-over. From the dual and chiral quark condensate one finds pseudo-critical temperatures of $198 , mathrm{MeV}$ and $170 , mathrm{MeV}$, respectively, for the deconfinement and chiral transition.
I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. 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 results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. For the chiral and deconfinement phase transition pseudo-critical temperatures of 170 MeV and 198 MeV, respectively, are obtained.
The canonical recursive Dyson--Schwinger equations for the three-gluon and ghost-gluon vertices are solved numerically. The employed truncation includes several previously neglected diagrams and includes back-coupling effects. We find an infrared finite ghost-gluon vertex and an infrared diverging three-gluon vertex. We also compare our results with those obtained in previous calculations, where bare vertices were used in the loop diagrams.
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