Theory of Casimir Forces: A Unified Approach Using Finite-Temperature Field Theory

TL;DR

The paper addresses a gauge‑invariant finite‑temperature description of Casimir forces between perfect electric conductors by deriving a stress tensor from first principles using Kapusta's finite‑temperature quantum field theory with Faddeev–Popov ghosts. It constructs a functional‑integral framework with explicit boundary conditions, obtains Green's functions for photons and ghosts, and applies Noether's theorem to define a gauge‑invariant stress tensor. The authors compute the Helmholtz free energy and extract normal and tangential Casimir stresses in a slit‑like pore, detailing zero and finite temperature limits as well as classical and quantum corrections, including disjoining pressures and vacuum contributions. The results demonstrate the essential role of ghost fields in canceling unphysical modes and provide a robust, modular approach that can be extended to other geometries, with potential impact on nanoengineered devices and surface phenomena.

Abstract

We present a quantum theory of Casimir forces between perfect electrical conductors, based on quantum electrodynamics and quantum statistical physics. This theory utilizes Kapusta's finite-temperature field theory, combined with the Faddeev-Popov ghost formalism. This approach allows us to calculate Casimir forces at finite temperatures, providing both previously known and new physical insights from a unified perspective. Furthermore, our method enables us to compute the stress tensor associated with Casimir forces, in accordance with the Helmholtz free energy of an equilibrium quantum electromagnetic field. Using this method, we calculate the tangential pressure in a slit-like pore due to the Casimir effect.