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


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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    • "Our variational approach has given a quite decent description of the infrared sector of Yang-Mills theory as, for example, a linearly rising non-Abelian Coulomb potential [5], an infrared diverging gluon energy (expressing confinement) [1] [5] in accord with lattice data [6], an infrared finite running coupling constant [7], a perimeter law for the 't Hooft loop [8], an area law for the Wilson loop [9] and a dielectric function of the Yang-Mills vacuum in accord with the bag model picture [10]. The obtained infrared behavior of ghost and gluon propagators were also found in a functional renormalization group approach [11] and supported by lattice calculation [6] [12]. "
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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.
    Full-text · Article · Oct 2013 · Physical Review D
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    ABSTRACT: We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in [1]. We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition. Comment: 15 pages
    Full-text · Article · Jul 2010 · European Physical Journal C
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    ABSTRACT: A general method to treat non-Gaussian vacuum wave functionals in the Hamiltonian formulation of a quantum field theory is presented. By means of Dyson--Schwinger techniques, the static Green functions are expressed in terms of the kernels arising in the Taylor expansion of the exponent of the vacuum wave functional. These kernels are then determined by minimizing the vacuum expectation value of the Hamiltonian. The method is applied to Yang--Mills theory in Coulomb gauge, using a vacuum wave functional whose exponent contains up to quartic terms in the gauge field. An estimate of the cubic and quartic interaction kernels is given using as input the gluon and ghost propagators found with a Gaussian wave functional. Comment: 27 pages, 21 figures
    Preview · Article · Sep 2010 · Physical review D: Particles and fields
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