Quantum electrodynamics of a free particle near dispersive dielectric or conducting boundaries

TL;DR

This paper investigates the quantum electrodynamics effects on a free electron near dielectric or conducting boundaries, deriving a formula for the inertial mass shift based on surface reflection coefficients, with applications to Casimir physics.

Contribution

It introduces a new approach to calculate the electron's mass shift near surfaces using reflection coefficients, extending the Lifshitz formula to quantum electrodynamics contexts.

Findings

Mass shift expressed via TE and TM reflection coefficients.

Exact results provided for various surface models.

Discussion of limitations and applications of the derived formula.

Abstract

Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over the TE and TM reflection coefficients associated with the surface, in analogy to the Lifshitz formula for the Casimir effect. We discuss the applications and potential limitations of this formula, and provide exact results for several models of the surface.