Finite-temperature Yang-Mills theory in the Hamiltonian approach in Coulomb gauge from a compactified spatial dimension

TL;DR

This paper develops a Hamiltonian approach to finite-temperature Yang-Mills theory by compactifying a spatial dimension, deriving equations that interpolate between zero and infinite temperature limits, and comparing propagators with grand canonical ensemble results.

Contribution

It introduces a novel Hamiltonian framework for finite-temperature Yang-Mills theory using spatial compactification and variational methods, connecting zero and high-temperature regimes.

Findings

Correct zero-temperature limit recovered

Equations reduce to 2+1-dimensional theory at high temperature

Propagators compared with grand canonical ensemble results

Abstract

Yang-Mills theory is studied at finite temperature within the Hamiltonian approach in Coulomb gauge by means of the variational principle using a Gaussian type ansatz for the vacuum wave functional. Temperature is introduced by compactifying one spatial dimension. As a consequence the finite temperature behavior is encoded in the vacuum wave functional calculated on the spatial manifold $\mathbb{R}^2 \times \mathrm {S}^1 (L)$ where $L^{-1}$ is the temperature. The finite-temperature equations of motion are obtained by minimizing the vacuum energy density to two-loop order. We show analytically that these equations yield the correct zero-temperature limit while at infinite temperature they reduce to the equations of the $2$+$1$-dimensional theory in accordance with dimensional reduction. The resulting propagators are compared to those obtained from the grand canonical ensemble where an additional ansatz for the density matrix is required.