Nonrelativistic noncommutative field theory and UV-IR mixing - art. no. 105006

We study a non-commutative non-relativistic scalar field theory in 2+1 dime nsions. 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 thermodyn amic potential at two-loop order. To avoid an IR singularity we have to int roduce 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.