The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem

TL;DR

This paper uses a path integral approach to rederive the Casimir energy for a sphere and a cylinder near a plane and calculates the first correction to the proximity force approximation.

Contribution

It introduces a new derivation method and provides the first correction terms to the proximity force theorem for these geometries.

Findings

Rederived Casimir energy expressions for sphere and cylinder configurations.

Calculated the first correction to the proximity force theorem.

Validated the correction through the path integral approach.

Abstract

Using a path integral approach we rederive a recently found representation of the Casimir energy for a sphere and a cylinder in front of a plane and derive the first correction to the proximity force theorem.