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

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 quantum 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 methodology, we calculate the excess surface tension on the walls of slit-like pores due to the Casimir effect.