Hamiltonian Flow of Yang-Mills Theory in Coulomb Gauge

Physical Review D - PHYS REV D 08/2010; 83(2). DOI: 10.1103/PHYSREVD.83.025010
Source: arXiv

ABSTRACT A new functional renormalization group equation for Hamiltonian Yang-Mills
theory in Coulomb gauge is presented and solved for the static gluon and ghost
propagators under the assumption of ghost dominance. The results are compared
to those obtained in the variational approach.

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    ABSTRACT: The deconfinement phase transition of SU(2) Yang-Mills theory is investigated in the Hamiltonian approach in Coulomb gauge assuming a quasi-particle picture for the grand canonical gluon ensemble. The thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. At the deconfinement phase transition the gluon energy, being infrared divergent in the confined phase, becomes infrared finite in the deconfined phase, while the ghost form factor remains infrared divergent in the deconfined phase but its infrared exponent is approximately halved. Using the lattice results for the gluon propagator to fix the scale the deconfinement transition temperature is obtained in the range of 275 to 290 MeV.
    Physical review D: Particles and fields 01/2013; 85(12). DOI:10.1103/PhysRevD.85.125029 · 4.86 Impact Factor
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    ABSTRACT: A numerical solution of the coupled Dyson-Schwinger equations for the ghost and gluon propagators in Yang-Mills theory is presented in Landau gauge. Aimed at investigating the infrared behavior of the propagators, the equations are simplified by neglecting the gluon loops, according to the ghost dominance hypothesis motivated by the Gribov-Zwanziger scenario. The equations are solved with an iterative method, eliminating the ultraviolet divergence through a continuous regulator function depending on the cut off scale. The solutions, derived for different values of the Euclidean space-time dimension, present scaling (the infrared exponents are obtained) or decoupling behavior, depending on whether the horizon condition is or not implemented. Moreover, it is shown that the running coupling constant approaches a constant value in the IR, corresponding to an attractive fixed point.
    Journal of Physics Conference Series 08/2012; 378(1). DOI:10.1088/1742-6596/378/1/012037
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    ABSTRACT: The variational approach to Yang-Mills theory in Coulomb gauge is extended to full QCD. For the quark sector we use a trial wave functional, which goes beyond the previously used BCS-type state and which explicitly contains the coupling of the quarks to transverse gluons. This quark wave functional contains two variational kernels: One is related to the quark condensate and occurs already in the BCS-type states. The other represents the form factor of the coupling of the quarks to the transverse gluons. Minimization of the energy density with respect to these kernels results in two coupled integral (gap) equations. These equations are solved numerically using the confining part of the non-Abelian color Coulomb potential and the lattice static gluon propagator as input. With the additional coupling of quarks to transverse gluons included the low energy chiral properties increase substantially towards their phenomenological values. We obtain a reasonable description of the chiral condensate, which for a vanishing current quark mass is obtained in the range of 190-235 MeV. The coupling of the quarks to the transverse gluons enhances the constituent quark mass by about 60% in comparison to the pure BCS ansatz.
    Physical Review D 10/2013; DOI:10.1103/PhysRevD.88.125021 · 4.86 Impact Factor

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