Worldline Approaches to Electromagnetic Casimir Interactions

The Casimir effect arises from quantum fluctuations of the electromagnetic field and leads to measurable forces between material bodies in vacuum. While Casimir forces between simple geometries have been well studied, accurately computing Casimir interactions in general or many-body configurations remains a challenging problem, particularly when electromagnetic vector properties and material responses are taken into account.

Among recent advances in computational approaches to Casimir physics, the worldline path-integral method provides a powerful alternative to traditional mode-summation and scattering techniques by reformulating the quantum vacuum energy in terms of an ensemble of fluctuating particle paths. This approach offers strong potential for treating arbitrary geometrical configurations through intuitive Monte Carlo sampling and highly parallelizable algorithms. 

In this work, we explore extensions of the worldline framework toward electromagnetic Casimir interactions in more general settings. We discuss how vector-field effects, polarization, and many-body contributions can be incorporated within a path-integral description, and we develop numerical strategies for efficiently evaluating electromagnetic Casimir observables within this framework. Representative configurations are used to illustrate the applicability of the method. Our results highlight both the capabilities and limitations of worldline-based approaches for electromagnetic Casimir physics and provide a flexible foundation for future theoretical and numerical developments.