Non-Relativistic Non-Commutative Field Theory and UV/IR Mixing

TL;DR

This paper investigates a non-commutative non-relativistic scalar field theory in 2+1 dimensions, analyzing UV/IR mixing, loop corrections, and thermodynamics, highlighting the role of chemical potential in non-planar contributions.

Contribution

It provides the first detailed analysis of UV/IR mixing and loop corrections in non-relativistic non-commutative field theories, emphasizing the impact of chemical potential.

Findings

UV/IR mixing observed in the theory.

One-loop two-point function correction is a delta function in momentum space.

Thermodynamic potential evaluated at two-loop order with chemical potential.

Abstract

We study a non-commutative non-relativistic scalar field theory in 2+1 dimensions. The theory shows the UV/IR mixing typical of QFT on non-commutative spaces. The one-loop correction to the two-point function turns out to be given by a delta-function in momentum space. The one-loop correction to the four-point function is of logarithmic type. We also evaluate the thermodynamic potential at two-loop order. To avoid an IR-singularity we have to introduce a chemical potential. The suppression of the non-planar contribution with respect to the planar one turns out to depend crucially on the value of the chemical potential.