The effective potential of the confinement order parameter in the Hamiltonian approach

Abstract

The effective potential of the order parameter for confinement is calculated for SU(N) Yang--Mills theory in the Hamiltonian approach. Compactifying one spatial dimension and using a background gauge fixing, this potential is obtained within a variational approach by minimizing the energy density for given background field. In this formulation the inverse length of the compactified dimension represents the temperature. Using Gaussian trial wave functionals we establish an analytic relation between the propagators in the background gauge at finite temperature and the corresponding zero-temperature propagators in Coulomb gauge. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. We explicitly show that the omission of the ghost drastically increases the transition temperature. From the full non-perturbative potential (with the ghost included) we extract a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV for SU(3).

26 pages, 17 eps figures

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Cited by in corpus (36)

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• Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
• A covariant variational approach to Yang-Mills Theory
• Two-colour QCD with heavy quarks at finite densities
• Yang-Mills correlators across the deconfinement phase transition
• Coulomb vs. physical string tension on the lattice
• Quark Sector of the QCD Groundstate in Coulomb Gauge
• Improved variational approach to QCD in Coulomb gauge
• Variational study of mass generation and deconfinement in Yang-Mills theory
• Vertex functions of Coulomb gauge Yang--Mills theory
• The BRST-invariant vacuum state of the Gribov-Zwanziger theory
• Covariant variational approach to Yang-Mills Theory: effective potential of the Polyakov loop
• A Gribov-Zwanziger type action invariant under background gauge transformations
• Finite-temperature Yang-Mills theory in the Hamiltonian approach in Coulomb gauge from a compactified spatial dimension
• Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified space
• Gauge copies in the Landau-DeWitt gauge: a background invariant restriction
• Chiral symmetry restoration at finite temperature within the Hamiltonian approach to QCD in Coulomb gauge
• Thermodynamics of an exactly solvable confining quark model
• Dyson--Schwinger approach to Hamiltonian Quantum Chromodynamics
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Effective Lagrangian for the Polyakov line on a lattice
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• The effective potential of the Polyakov loop in the Hamiltonian approach to QCD
• Regimes of $3D$ Yang--Mills theory in the presence of a constant vector background
• Polyakov Loop in Non-covariant Operator Formalism
• Hamiltonian approach to QCD in Coulomb gauge: Gribov's confinement scenario at work
• Confinement/deconfinement transition temperature from the Polyakov loop potential and gauge-invariant gluon mass
• Hamiltonian approach to QCD in Coulomb gauge: From the vacuum to finite temperatures
• Deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
• The scalar sunset diagram at finite temperature with imaginary square masses
• Gribov horizon, Polyakov loop and finite temperature