Casimir effect via a generalized Matsubara formalism

TL;DR

This paper explores the Casimir effect in systems with complex topologies using a generalized Matsubara formalism, accounting for both spatial constraints and thermal effects in scalar fields across multiple dimensions.

Contribution

It introduces a novel approach combining spatial and thermal effects in the Casimir effect analysis through a generalized Matsubara formalism for scalar fields.

Findings

Derived Casimir pressure in heated systems between infinite planes.

Compared results with existing literature, confirming consistency.

Extended understanding of Casimir effect in nontrivial topologies.

Abstract

We investigate the Casimir effect in the context of a nontrivial topology by means of a generalized Matsubara formalism. This is performed in the context of a scalar field in $D$ Euclidean spatial dimensions with $d$ compactified dimensions. The procedure gives us the advantage of considering simultaneously spatial constraints and thermal effects. In this sense, the Casimir pressure in a heated system between two infinite planes is obtained and the results are compared with those found in the literature.