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.
Cabral et al. (Sun,) studied this question.