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

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 θ-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.

arXiv comment41 pages

References in corpus (26)

• Gauge Theory Correlators from Non-Critical String Theory
• New Developments in the Casimir Effect
• Zeta Functions and the Casimir Energy
• Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section
• Spectral functions in mathematics and physics
• Casimir Forces in a Piston Geometry at Zero and Finite Temperatures
• Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields
• Thermal Casimir effect in ideal metal rectangular boxes
• Geometry effects in confined space
• Kaluza-Klein models as pistons
• Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique
• The heat kernel expansion for the electromagnetic field in a cavity
• Thermal Casimir effect for neutrino and electromagnetic fields in closed Friedmann cosmological model
• Entropy Bounds in $R\times S^3$ Geometries
• Finite temperature Casimir effect in piston geometry and its classical limit
• Generalized Stochastic Quantization of Yang-Mills Theory
• Zeta function regularization for a scalar field in a compact domain
• Zero modes, entropy bounds and partition functions
• The thermal energy of a scalar field in a one-dimensional compact space
• Functional integration and gauge ambiguities in generalized abelian gauge theories
• Witten-Veneziano Relation for the Schwinger Model
• Global Path Integral Quantization of Yang-Mills Theory
• Geometry of the Casimir Effect
• Abelian gauge theories on compact manifolds and the Gribov ambiguity
• On the minima and convexity of Epstein Zeta function
• Analytical and differential - algebraic properties of Gamma function

Cited by in corpus (3)

• Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold
• Maxwell Theory on a Compact Manifold as a Topologically Ordered System
• Aspects of Higher-Abelian Gauge Theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops