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

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.

10 pages, 7 figures

References in corpus (9)

• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Coulomb gauge gluon propagator and the Gribov formula
• Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
• Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
• Dielectric function of the QCD vacuum
• The 't Hooft loop in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
• Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum
• Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory
• The Yang-Mills Vacuum in Coulomb Gauge in D=2+1 Dimensions

Cited by in corpus (5)

• The nonperturbative functional renormalization group and its applications
• The UV sensitivity of the Higgs potential in Gauge-Higgs Unification
• The effective potential of the Polyakov loop in the Hamiltonian approach to QCD
• Gribov horizon, Polyakov loop and finite temperature
• Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions