Remarks on the thermodynamics and the vacuum energy of a quantum Maxwell gas on compact and closed manifolds

TL;DR

This paper investigates how the topology of compact, closed manifolds influences the thermodynamics and vacuum energy of a quantum Maxwell gas, resolving quantization ambiguities and providing explicit thermodynamic formulas.

Contribution

It clarifies the relationship between topology and thermodynamics in quantum Maxwell theory, resolving the Gribov problem and comparing quantization schemes.

Findings

Topology affects vacuum energy and thermal excitations.

Explicit formulas for thermodynamic functions on n-torus.

Resolution of gauge quantization ambiguities.

Abstract

The quantum Maxwell theory at finite temperature at equilibrium is studied on compact and closed manifolds in both the functional integral- and Hamiltonian formalism. The aim is to shed some light onto the interrelation between the topology of the spatial background and the thermodynamic properties of the system. The quantization is not unique and gives rise to inequivalent quantum theories which are classified by {\theta}-vacua. Based on explicit parametrizations of the gauge orbit space in the functional integral approach and of the physical phase space in the canonical quantization scheme, the Gribov problem is resolved and the equivalence of both quantization schemes is elucidated. Using zeta-function regularization the free energy is determined and the effect of the topology of the spatial manifold on the vacuum energy and on the thermal gauge field excitations is clarified. The general results are then applied to a quantum Maxwell gas on a n-dimensional torus providing explicit formulae for the main thermodynamic functions in the low- and high temperature regimes, respectively.