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

J. Heffner and H. Reinhardt
Phys. Rev. D 91, 085022 – Published 16 April 2015

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 R2×S1(L) where L1 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.

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  • Received 26 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.085022

© 2015 American Physical Society

Authors & Affiliations

J. Heffner* and H. Reinhardt

  • Institut für Theoretische Physik, Eberhard-Karls-Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany

  • *jan.heffner@uni-tuebingen.de
  • hugo.reinhardt@uni-tubeingen.de

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Vol. 91, Iss. 8 — 15 April 2015

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