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

摘要

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