Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified space

Abstract

The partition function of a relativistic invariant quantum field theory is expressed by its vacuum energy calculated on a spatial manifold with one dimension compactified to a 1-sphere $S^1(\beta )$, whose circumference $\beta$ represents the inverse temperature. Explicit expressions for the usual energy density and pressure in terms of the energy density on the partially compactified spatial manifold ${\mathbb{R}}^2\times S^1(\beta )$ are derived. To make the resulting expressions mathematically well-defined a Poisson resummation of the Matsubara sums as well as an analytic continuation in the chemical potential are required. The new approach to finite-temperature quantum field theories is advantageous in a Hamilton formulation since it does not require the usual thermal averages with the density operator. Instead, the whole finite-temperature behaviour is encoded in the vacuum wave functional on the spatial manifold ${\mathbb{R}}^2\times S^1(\beta )$. We illustrate this approach by calculating the pressure of a relativistic Bose and Fermi gas and reproduce the known results obtained from the usual grand canonical ensemble. As a first non-trivial application we calculate the pressure of Yang-Mills theory as function of the temperature in a quasi-particle approximation motivated by variational calculations in Coulomb gauge.

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Cited by in corpus (8)

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• Covariant variational approach to Yang-Mills Theory: Thermodynamics
• Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge
• Center phase transition from matter propagators in (scalar) QCD
• The UV sensitivity of the Higgs potential in Gauge-Higgs Unification
• The effective potential of the Polyakov loop in the Hamiltonian approach to QCD
• On Quantum Fields at High Temperature