Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions

TL;DR

This paper calculates the radiative correction to the Casimir energy for Lorentz-violating scalar fields in various dimensions, using boundary conditions and regularization techniques, revealing consistent and convergent results.

Contribution

It introduces a method to compute radiative corrections to Casimir energy for Lorentz-violating fields with boundary conditions, employing position-dependent counterterms and regularization.

Findings

Results are convergent and physically consistent across dimensions.

Casimir energy density varies with Lorentz violation type and dimension.

Plots illustrate differences between time-like and space-like Lorentz violation.

Abstract

The renormalization program in every renormalized theory should be run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In the present study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentz-violating scalar field constrained with Dirichlet boundary condition between two parallel plates in d spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme supplemented by the cutoff regularization technique and analytic continuation technique were employed. Normally, in the box subtraction scheme, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.