Noncommutative scalar fields in compact spaces: Quantization and implications

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 others'. It is found that thermodynamic quantities in noncommutative models, irrespective of whether the model is more deformed in the infrared/UV region, show deviation from standard results in the high temperature region.