Vacuum Energy and Topological Mass in Interacting Elko and Scalar Field Theories

TL;DR

This paper investigates the Casimir effect in a four-dimensional system with Elko fermionic and scalar fields, analyzing vacuum energy, mass corrections, and boundary effects using the effective potential formalism.

Contribution

It introduces a detailed analysis of vacuum energy and topological mass corrections for Elko and scalar fields with boundary conditions, a novel application in this context.

Findings

Calculated vacuum energy density and first-order correction.

Determined the topological mass dependence on boundary conditions.

Analyzed the impact of coupling constants on mass corrections.

Abstract

In this paper, we consider a four-dimensional system composed of a mass-dimension-one fermionic field, also known as Elko, interacting with a real scalar field. Our main objective is to analyze the Casimir effects associated with this system, assuming that both the Elko and scalar fields satisfy Dirichlet boundary conditions on two large parallel plates separated by a distance $L$. In this scenario, we calculate the vacuum energy density and its first-order correction in the coupling constants of the theory. Additionally, we consider the mass correction for each field separately, namely the topological mass that arises from the boundary conditions imposed on the fields and which also depends on the coupling constants. To develop this analysis, we use the mathematical formalism known as the effective potential, expressed as a path integral in quantum field theory.