Thermal and Casimir effects in a Lorentz-violating massive scalar field

TL;DR

This work investigates how Lorentz violation in a massive scalar field, implemented via the SME background $k^{\mu\nu}$, modifies thermal and finite-size quantum fluctuations. Using Thermo Field Dynamics on topologies that encode temperature and spatial confinement, the authors derive a LV-modified propagator and energy-momentum tensor, enabling a unified treatment of thermal and boundary effects. They obtain explicit LV corrections to the Stefan-Boltzmann-type law and to the Casimir energy and pressure at zero and finite temperature, with anisotropy determined by the components of $k^{\mu\nu}$. The results highlight how temperature and finite-size effects interplay with LV backgrounds, providing directional signatures that could guide precision Casimir and thermal tests of LV physics within the SME framework.

Abstract

In this work, a massive scalar field theory incorporating Lorentz violation is investigated. The symmetry breaking is introduced via a background traceless antisymmetric tensor. Within the framework of Thermo Field Dynamics (TFD), the effects of space-time compactification are explored, allowing the simultaneous treatment of thermal and finite-size phenomena. The resulting modifications to the energy-momentum tensor and Feynman propagator are analyzed, leading to Lorentz-violating corrections to the Stefan-Boltzmann law and the Casimir effect. This unified approach highlights the interplay between temperature, spatial constraints, and Lorentz-violating backgrounds in shaping the behavior of quantum fields.