# The Casimir effect for the scalar and Elko fields in a Lifshitz-like field theory

## TL;DR

This paper calculates the Casimir energy for scalar and Elko fields in a Lifshitz-like field theory, analyzing massless and massive cases, and explores the impact of Lifshitz parameters on thermal corrections.

## Contribution

It provides the first detailed calculation of Casimir energy for scalar and Elko fields at a Lifshitz fixed point, including thermal effects and dimensional regularization.

## Key findings

- Casimir energy expressed in terms of Lifshitz and dimensional parameters
- Recovery of standard results in the absence of Lifshitz parameters
- Lifshitz parameter influences thermal corrections for massless scalar fields

## Abstract

In this work, we obtain the Casimir energy for the real scalar field and the Elko neutral spinor field in a field theory at a Lifshitz fixed point (LP). We analyze the massless and the massive case for both fields using dimensional regularization. We obtain the Casimir energy in terms of the dimensional parameter and the LP parameter. Particularizing our result, we can recover the usual results without LP parameter in (3+1) dimensions presented in the literature. Moreover, we compute the effects of the LP parameter in the thermal corrections for the massless scalar field.