Path-integral approach to Casimir effect with infinitely thin plates

TL;DR

This paper investigates the use of path-integral methods with Dirac-delta boundary conditions to analyze the Casimir effect, examining the approach's limitations across various boundary scenarios.

Contribution

It explores the boundaries and limitations of the path-integral approach with delta functions for modeling the Casimir effect with thin plates.

Findings

Identifies conditions where the path-integral approach is valid

Highlights limitations under certain boundary conditions

Provides insights into boundary condition modeling in quantum field theory

Abstract

When studying the Casimir effect in a quantum field theory setting, one can impose the boundary conditions by adding appropriate Dirac-delta functions to the path integral. In this paper, the limits of this approach are explored under different boundary conditions.