The field theoretic derivation of the contact value theorem in planar geometries and its modification by the Casimir effect

TL;DR

This paper derives the contact value theorem for Coulomb gases in planar geometries using field theory and reveals a Casimir-like fluctuation term when dielectric properties differ.

Contribution

It provides a field theoretic derivation of the contact value theorem and introduces a modification accounting for dielectric mismatch effects via the Casimir effect.

Findings

Derivation of the contact value theorem using Hamiltonian field theory.

Identification of a Casimir-like fluctuation term due to dielectric mismatch.

Extension of the theorem to include fluctuation effects in planar geometries.

Abstract

The contact value theorem for Coulomb gases in planar or film-like geometries is derived using a Hamiltonian field theoretic representation of the system. The case where the film is enclosed by a material of different dielectric constant to that of the film is shown to contain an additional Casimir-like term which is generated by fluctuations of the electric potential about its mean-field value.