Analysis of scalar and fermion quantum field theory on anti-de Sitter space-time

Abstract

We study vacuum and thermal expectation values of quantum scalar and Dirac fermion fields on anti-de Sitter space-time. Anti-de Sitter space-time is maximally symmetric and this enables expressions for the scalar and fermion vacuum Feynman Green's functions to be derived in closed form. We employ Hadamard renormalization to find the vacuum expectation values. The thermal Feynman Green's functions are constructed from the vacuum Feynman Green's functions using the imaginary time periodicity/anti-periodicity property for scalars/fermions. Focussing on massless fields with either conformal or minimal coupling to the space-time curvature (these two cases being the same for fermions) we compute the differences between the thermal and vacuum expectation values. We compare the resulting energy densities, pressures and pressure deviators with the corresponding classical quantities calculated using relativistic kinetic theory.

30 pages, 10 figures, minor changes, to appear in the Proceedings of the Fourth Amazonian Symposium on Physics, Belem, Brazil, 18-22 September 2017

References in corpus (9)

• Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid
• Hadamard renormalized scalar field theory on anti-de Sitter space-time
• Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases
• Thermal expectation values of fermions on anti-de Sitter space-time
• Dirac fermions on an anti-de Sitter background
• Quantum non-equilibrium effects in rigidly-rotating thermal states
• Anti-de Sitter relativity
• Quantum corrections in thermal states of fermions on anti-de Sitter space-time
• Covariant fields on anti-de Sitter spacetimes

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• Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension
• Vortical Effects for Free Fermions on Anti-De Sitter Space-Time
• Non-singular T-K axion stars with/without the dynamical bosonic field in the presence of negative $\Lambda$ term