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

Abstract

We study vacuum and thermal expectation values of quantum scalar and Dirac fermion fields on anti-de Sitter (adS) spacetime. AdS spacetime 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 (v.e.v.s). 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. Focusing on massless fields with either conformal or minimal coupling to the spacetime curvature (these two cases being the same for fermions) we compute the differences between the thermal expectation values and v.e.v.s. We compare the resulting energy densities, pressures and pressure deviators with the corresponding classical quantities calculated using relativistic kinetic theory.