Vacuum energy density for interacting real and complex scalar fields in a Lorentz symmetry violation scenario

TL;DR

This paper analyzes how Lorentz symmetry violation influences the vacuum energy density and topological mass in a system of interacting real and complex scalar fields with specific boundary conditions, using effective potential methods.

Contribution

It introduces an analytical framework to evaluate vacuum energy and topological mass in Lorentz-violating scenarios with interacting scalar fields under different boundary conditions.

Findings

Lorentz violation affects vacuum energy density and mass generation.

Different vacuum states depend on Lorentz violation parameters.

Analytical expressions for loop corrections are derived.

Abstract

In this paper the vacuum energy density and generation of topological mass are investigated for a system of a real and complex scalar fields interacting with each other. In addition to that, it is also included the quartic self-interaction for each one of the fields. The condition imposed on the real field is the periodic condition, while the complex field obey a quasi-periodic condition. The system is placed in a scenario where the CPT-even aether-type Lorentz symmetry violation takes place. We allow that the Lorentz violation affects the fields with different intensities. The vacuum energy density, its loop correction, and the topological mass are evaluated analytically. It is also discussed the possibility of different vacuum states and their corresponding stability requirements, which depends on the conditions imposed on the fields, the interaction coupling constants and also the Lorentz violation parameters. The formalism used here to perform this investigation is the effective potential one, which is written as a loop expansion via path integral in quantum field theory.