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

TL;DR

This paper derives explicit formulas for vacuum and thermal expectation values of scalar and fermion fields in anti-de Sitter space-time, comparing quantum results with classical kinetic theory predictions.

Contribution

It provides closed-form expressions for quantum Green's functions and expectation values in AdS space, including thermal effects for massless fields with different couplings.

Findings

Explicit vacuum Green's functions derived for scalar and fermion fields.

Thermal expectation values computed and compared with classical theory.

Results highlight differences between quantum and classical energy-momentum quantities.

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.