Casimir Energy for Lorentz-Violating Scalar Field with Helical Boundary Condition in d Spatial Dimensions

TL;DR

This paper investigates the Casimir energy for Lorentz-violating scalar fields with helical boundary conditions in arbitrary spatial dimensions, including thermal and radiative corrections, ensuring consistency with boundary conditions and exploring effects of Lorentz violation.

Contribution

It introduces a novel calculation of Casimir energy with Lorentz violation and helical boundary conditions across multiple dimensions, including one-loop corrections with position-dependent counterterms.

Findings

Results are consistent with physical expectations across dimensions.

Graphical analysis of Casimir energy density for Lorentz violations.

Convergence of the Casimir energy calculations with established theories.

Abstract

Delving into spring-like helical configurations, such as DNA within our cells, motivates physicists to inquire about the effects of such structures in the realm of quantum field theory, specifically unraveling their manifestation of effectiveness in Casimir energy. To explore this, we initiated our investigation with the Casimir effect and proceeded to calculate the Casimir energy, along with its thermal and radiative corrections, for massive and massless Lorentz-violating scalar fields across $d+1$ dimensional space-time. Adhering to the principle that the renormalization program should be consistent with the boundary conditions applied to the quantum fields was paramount. Accordingly, one-loop correction to the Casimir energy for both massive and massless scalar fields under helical boundary conditions by employing a position-dependent counterterm was performed. Our results, spanning across spatial dimensions, exhibited convergence and coherence with established physical grounds. Additionally, we presented the Casimir energy density using graphical plots for systems featuring time-like and space-like Lorentz violations across all spatial dimensions, followed by a comprehensive discussion of the obtained results.