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28 March 2024
 
  » arxiv » 1501.5858

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Finite-temperature Yang-Mills theory in the Hamiltonian approach in Coulomb gauge from a compactified spatial dimension
J. Heffner ; H. Reinhardt ;
Date 23 Jan 2015
AbstractYang-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 $mathbb{R}^2 imes mathrm {S}^1 (L)$ 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.
Source arXiv, 1501.5858
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