TFD formalism: applications to the scalar field in a Lorentz-violating theory

TL;DR

This paper explores the Thermofield Dynamics formalism applied to a Lorentz-violating scalar field theory, demonstrating its advantages over Matsubara formalism in calculating thermal effects like Stefan-Boltzmann law and Casimir effect.

Contribution

It introduces a Lorentz-breaking scalar field theory within the TFD formalism and compares its topological flexibility to the Matsubara approach, enabling unified treatment of thermal phenomena.

Findings

Calculated Stefan-Boltzmann law at finite temperature.

Derived Casimir effect at zero and non-zero temperature.

Demonstrated TFD's flexibility with different topologies.

Abstract

The Thermofield Dynamics (TFD) formalism is considered. In this context, a Lorentz-breaking scalar field theory is introduced. In contrast to the Matsubara formalism, the best-known approach to introducing the temperature effect, TFD is a real-time formalism and is a topological field theory. While in Matsubara the temperature effects are introduced as a consequence of a compactification of the field in a finite interval on the time axis, in the TFD this effect emerges through a condensed state related to the Bogoliubov transformation. An advantage of the TFD formalism is that different topologies, which lead to different effects, can be chosen. Here, three different topologies are considered. Then the Stefan-Boltzmann law and Casimir effect at zero and non-zero temperature are calculated. This is a unique feature of TFD, which allows us to treat different phenomena in the same way.