Explorando a termodinâmica de campos escalares não comutativos.

Abstract

In this work, we study the thermo dynamic properties of the Bose-Einstein condensation (BEC) for a relativistic Bose gas in the context of the non commutative quantum field theory. Such theories was introduced as a generalization of quantum mechanics on a non commutative space time. Our main goal is to investigate in which temperature and/or energy regimes the non commutativity can characterize some influence in the properties of Bose-Einstein condensation described by a relativistic bosonic gas. We use a non com- mutative bosonic field theory introducing the non commutative parameters θ and σ. Both parameters play a key role in the modified dispersion relations of the non commutative bosonic field, leading to possibles triking consequences for phenomenology. Analytical expressions for the condensate fraction, internal energy, pressure and specifiche at of the system are obtained by expanding in a power series of the non commutative parameters. These results are compared with that one get by numerical methods. The non commuta- tive effects in the thermo dynamic properties of the system are discussed, then is found that the non commutativity exhibit caracteristics important at high temperature.