# Casimir forces between spheres and loop integrals

## TL;DR

This paper reviews recent methods for calculating Casimir forces between dielectric spheres, emphasizing direct force evaluation via stress tensors and introducing a loop integral formulation for effective field propagation.

## Contribution

It presents a novel approach to compute Casimir forces directly from stress tensors and develops a loop integral framework for analyzing electromagnetic field interactions.

## Key findings

- Force calculations via stress tensor are effective for dielectric spheres
- Loop integral formulation offers a new perspective on field propagation
- The methods facilitate more accurate Casimir force predictions

## Abstract

A summary of recent calculations of Casimir forces between a collection of $N$-dielectric spheres is presented. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. A loop integral formulation is also discussed where we rewrite the expressions for the force in terms of loop integrals for the effective classical propagation of the electric and magnetic fields.