Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution

TL;DR

This paper reviews the development and application of zeta function regularization methods in quantum physics, highlighting Dowker's influential contributions to Casimir effect calculations and discussing recent advances in operator regularization.

Contribution

It provides a comprehensive overview of the historical and technical development of zeta function regularization, emphasizing Dowker's pivotal role and recent progress in operator regularization techniques.

Findings

Zeta function regularization is a powerful method for quantum vacuum calculations.

Dowker's work significantly advanced the application of zeta functions in physics.

Recent results include new operator regularization procedures.

Abstract

A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a number of the strengths of this powerful and elegant method, some of its limitations are discussed. Finally, recent results of the so called operator regularization procedure are presented.