Casimir forces in a T operator approach

TL;DR

This paper develops a scattering approach to Casimir forces using transition operators, demonstrating how to compute forces between objects like spheres at all distances through scattering data.

Contribution

It introduces a method to calculate Casimir forces via transition operators, expanding the applicability of scattering techniques to complex geometries.

Findings

Validated the approach with 1D and 3D examples

Showed how to compute forces between spherical bodies at all distances

Analyzed convergence properties of the formula

Abstract

We explore the scattering approach to Casimir forces. Our main tool is the description of Casimir energy in terms of transition operators, as presented in Kenneth and Klich, Phys. Rev. Lett. 97, 160401 (2006). We study the convergence properties of the formula and how to utilize it, together with scattering data to compute the force. We illustrate the approach by describing the force between scatterers in 1d and 3d,, and in particular show how it may be applied in order to study the interaction between two spherical bodies at all distances.