Lifshitz Formula Using Box Renormalization (In Persian)

TL;DR

This paper rigorously derives the Lifshitz formula for Casimir energy between two dielectrics at zero temperature using box renormalization, providing a clear and unambiguous method to handle infinities in the energy calculation.

Contribution

It presents the first systematic and rigorous derivation of Casimir energy using box renormalization, addressing ambiguities present in previous methods.

Findings

Systematic removal of infinities in Casimir energy calculation

Demonstration of the accuracy of box renormalization scheme

First unambiguous derivation of Casimir energy for dielectrics

Abstract

In this paper the Lifshitz formula for the Casimir energy between two dielectrics in zero temperature is derived using box renormalization. Although there are several derivations for the force in this case in the literature, including Lifshitz's own proof, so far there has been no unambiguous and rigorous derivation for energy that we are aware of. Since the energy becomes important in some cases, e.g. calculation of entropy or heat capacity, using the correct and precise definition of the Casimir energy, for the first time, we remove all of the infinities systematically without any ambiguity. This proof also shows the strength and accuracy of the box renormalization scheme.