A diagrammatic expansion of the Casimir energy in multiple reflections: theory and applications

TL;DR

This paper introduces a diagrammatic method to compute Casimir energies in multi-object systems, simplifying calculations of complex interactions and enabling analytical solutions for configurations like edges and needles.

Contribution

It presents a novel diagrammatic expansion for Casimir energy calculations, facilitating analytical and organized multi-reflection analysis in multibody configurations.

Findings

Analytical formulas for edge-edge Casimir interactions.

First example of blocking effects in Casimir energy.

Description of Casimir repulsion in a recent model.

Abstract

We develop a diagrammatic representation of the Casimir energy of a multibody configuration. The diagrams represent multiple reflections between the objects and can be organized by a few simple rules. The lowest-order diagrams (or reflections) give the main contribution to the Casimir interaction which proves the usefulness of this expansion. Among some applications of this, we find analytical formulae describing the interaction between "edges", i.e. semi-infinite plates, where we also give a first example of blocking in the context of the Casimir energy. We also find the interaction of edges with a needle and describe analytically a recent model of the repulsion due to the Casimir interaction.