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

TL;DR

This paper calculates the effective potential for the confinement order parameter in SU(N) Yang-Mills theory using a Hamiltonian approach with a compactified spatial dimension, revealing insights into the deconfinement phase transition.

Contribution

It introduces a variational Hamiltonian method to compute the confinement potential at finite temperature, including ghost effects, and determines critical temperatures for SU(2) and SU(3).

Findings

Recover the Weiss potential in a simplified truncation.

Omission of ghosts increases the transition temperature.

Critical temperatures are 269 MeV for SU(2) and 283 MeV for SU(3).

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).