Local zeta regularization and the scalar Casimir effect II. Some explicitly solvable cases

TL;DR

This paper applies a formalism for scalar field vacuum effects using local zeta regularization to explicitly solvable configurations like planes and wedges, providing analytical solutions and insights.

Contribution

It demonstrates the application of the zeta regularization formalism to specific geometries, offering explicit analytical solutions for the scalar Casimir effect.

Findings

Explicit solutions for parallel and perpendicular planes

Analysis of the three-dimensional wedge case

Validation of the formalism through solvable examples

Abstract

In Part I of this series of papers we have described a general formalism to compute the vacuum effects of a scalar field via local (or global) zeta regularization. In the present Part II we exemplify the general formalism in a number of cases which can be solved explicitly by analytical means. More in detail we deal with configurations involving parallel or perpendicular planes and we also discuss the case of a three-dimensional wedge.