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

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.