Towards a Theory of Molecular Forces between Deformed Media

TL;DR

This paper develops a comprehensive macroscopic theory for molecular and Casimir forces between arbitrarily shaped dielectric surfaces, unifying and extending existing models through a path integral approach.

Contribution

It introduces a general path integral framework to compute electromagnetic fluctuation-induced forces for deformed dielectric media without shape or material independence assumptions.

Findings

Derives an effective Gaussian action for force calculation.

Recovers Lifshitz theory for flat surfaces.

Provides explicit results for ideal metals with deformed surfaces.

Abstract

A macroscopic theory for the molecular or Casimir interaction of dielectric materials with arbitrarily shaped surfaces is developed. The interaction is generated by the quantum and thermal fluctuations of the electromagnetic field which depend on the dielectric function of the materials. Using a path integral approach for the electromagnetic gauge field, we derive an effective Gaussian action which can be used to compute the force between the objects. No assumptions about the independence of the shape and material dependent contributions to the interaction are made. In the limiting case of flat surfaces our approach yields a simple and compact derivation of the Lifshitz theory for molecular forces. For ideal metals with arbitrarily deformed surfaces the effective action can be calculated explicitly. For the general case of deformed dielectric materials the applicability of perturbation theory and numerical techniques to the evaluation of the force from the effective action is discussed.