Radiative corrections to the Casimir energy in the $\lambda|\phi|^{4}$ model under quasi-periodic boundary conditions

TL;DR

This paper calculates the first radiative correction to the Casimir energy in a quantum field theory with quasi-periodic boundary conditions, extending previous results for periodic and anti-periodic cases.

Contribution

It provides the first computation of radiative corrections to Casimir energy under quasi-periodic boundary conditions in a $oxed{ ext{scalar}}$ field theory.

Findings

Results agree with known cases for periodic and anti-periodic boundary conditions.

Extends the understanding of Casimir energy corrections to more general boundary conditions.

Provides a basis for further studies in quantum field theories with complex boundary conditions.

Abstract

We compute the first radiative correction to the Casimir energy in the $(d+1)$-dimensional $\lambda|\phi|^{4}$ model submitted to quasi-periodic boundary conditions in one spatial direction. Our results agree with the ones found in the literature for periodic and anti-periodic boundary conditions, special cases of the quasi-periodic boundary conditions.