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

Understand

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.