Renormalised fermion vacuum expectation values on anti-de Sitter space-time

TL;DR

This paper computes renormalised vacuum expectation values for fermion fields in four-dimensional anti-de Sitter space-time using multiple regularisation methods, providing insights into quantum field behavior in curved backgrounds.

Contribution

It introduces a comprehensive comparison of renormalisation techniques for fermion vacuum expectation values in anti-de Sitter space.

Findings

Consistent results across different regularisation methods.

Explicit expressions for fermion condensate, charge current, and stress-energy tensor.

Enhanced understanding of quantum effects in curved space-time.

Abstract

The Schwinger-de Witt and Hadamard methods are used to obtain renormalised vacuum expectation values for the fermion condensate, charge current and stress-energy tensor of a quantum fermion field of arbitrary mass on four-dimensional anti-de Sitter space-time. The quantum field is in the global anti-de Sitter vacuum state. The results are compared with those obtained using the Pauli-Villars and zeta-function regularisation methods, respectively.