Noncommutative scalar fields in compact spaces: quantisation and implications

TL;DR

This paper investigates a two-component scalar field theory with momentum space noncommutativity in a compact setting, revealing energy level splitting and thermodynamic deviations at high temperatures due to noncommutative effects.

Contribution

It introduces a quantization method for noncommutative scalar fields in compact spaces and analyzes the resulting energy spectrum and thermodynamic properties.

Findings

Energy levels of modes are split due to noncommutativity.

Thermodynamic quantities deviate from standard results at high temperatures.

Deformed dispersion relations influence thermal behavior.

Abstract

In this paper we consider a two component scalar field theory, with noncommutativity in its conjugate momentum space. We quantize such a theory in a compact space with the help of dressing transformations and we reveal a significant effect of introducing such noncommutativity as the splitting of the energy levels of each individual mode that constitutes the whole system. We further compute the thermal partition function exactly with predicted deformed dispersion relations from noncommutative theories and compare the results with usual results. It is found that thermodynamic quantities in noncommutative models, irrespective of whether the model is more deformed in infrared/UV region, show deviation from standard results in high temperature region.