Exploring the thermodynamics of non-commutative scalar fields

TL;DR

This paper investigates how non-commutative geometry influences the thermodynamic behavior of relativistic Bose-Einstein condensates, revealing signatures near the critical temperature due to modified dispersion relations.

Contribution

It introduces a study of non-commutative effects on BEC thermodynamics, deriving key properties and analyzing their behavior in relativistic regimes.

Findings

Non-commutativity affects condensate fraction, energy, pressure, and heat capacity.

Signatures of non-commutativity emerge around the critical temperature.

Modified dispersion relations lead to new phenomenological insights.

Abstract

We study the thermodynamic properties of the Bose-Einstein condensate (BEC) in the context of the quantum field theory with non-commutative target space. Our main goal is to investigate in which temperature and/or energy regimes the non-commutativity can characterize some influence in the BEC properties described by a relativistic massive non-commutative boson gas. The non-commutativity parameters play a key role in the modified dispersion relations of the non-commutative fields, leading to a new phenomenology. We have obtained the condensate fraction, internal energy, pressure and specific heat of the system and taken ultra-relativistic (UR) and non-relativistic limits (NR). The non-commutative effects in the thermodynamic properties of the system are discussed. We found that there appear interesting signatures around the critical temperature.