A perturbative approach to calculating the Casimir force in fluctuating scalar and vector fields

TL;DR

This paper introduces a perturbative series expansion method to calculate the Casimir force between objects in scalar or vector fluctuating fields, including finite-temperature effects and massive vector field generalizations.

Contribution

It presents a novel perturbative approach for Casimir force calculations applicable to arbitrary shapes, dimensions, and field types, extending existing scattering methods.

Findings

Derived a series expansion in susceptibility for Casimir force

Included finite-temperature corrections in the analysis

Extended the method to massive vector fields

Abstract

Based on a perturbative approach, a series expansion in susceptibility function of the medium is obtained for the Casimir force between arbitrary shaped objects immersed in a scalar or vector fluctuating field in arbitrary dimensions. Finite-temperature corrections are derived and the results are compared in first order with weak coupling regime in scattering method. The generalization to a massive vector field is also investigated.