Reworking the Antonsen-Bormann idea

TL;DR

This paper revisits the Antonsen-Bormann approach to compute the zeta function for a scalar field in curved space, employing the Schwinger operator expansion to enhance understanding of quantum field theory in curved backgrounds.

Contribution

It introduces a novel application of the Antonsen-Bormann idea to calculate the zeta function using the Schwinger operator expansion, expanding its utility beyond previous uses.

Findings

Successfully computes the zeta function for a scalar field in curved space.

Demonstrates the effectiveness of the Schwinger operator expansion in this context.

Provides a new methodological approach for quantum field theory in curved backgrounds.

Abstract

The Antonsen - Bormann idea was originally proposed by these authors for the computation of the heat kernel in curved space; it was also used by the author recently with the same objective but for the Lagrangian density for a real massive scalar field in 2 + 1 dimensional curved space. It is now reworked here with a different purpose - namely, to determine the zeta function for the said model using the Schwinger operator expansion.