Thermal aspects of field theories

Abstract

This thesis focus on examining the thermodynamic properties of various prominent field theories concerning high-energy and condensed matter physics. We make the usage of the theory of ensembles to perform our analysis. At the beginning, we supply the thermodynamic properties based on the formalism of canonical ensemble to the Aharonov-Bohm quantum ring considering both scenarios: the relativistic and the non-relativistic cases. Next, we construct a model in order to study quantum gases. In this context, we examine bosons, fermions and spinless particles within the grand-canonical ensemble taking into account two different approaches: interacting and noninteracting particles. To corroborate our results, we apply them to the Bose-Einstein condensate and to the helium dimmers. The same approach is applied considering rather Lorentz violation. Moreover, in this context, we also propose two applications to support our theoretical calculations: phosphorene layers and spin precession of quantum gases. Next, the thermodynamic properties are investigated as well to a variety of models/theories (regarding different energy dispersion relations) when the Lorentz symmetry is no longer maintained within the canonical ensemble formalism. To these cases, three distinct thermal scenarios of the universe are considered: the cosmic microwave background, the electroweak epoch, and the inflationary period.