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Nonrelativistic noncommutative field theory and UV-IR mixing
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We study a non-commutative non-relativistic scalar field theory in 211 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 d 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.
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GOMIS TORNÉ, Joaquim, LANDSTEINER, Karl and LÓPEZ, Esperanza. Nonrelativistic noncommutative field theory and UV-IR mixing. Physical Review D. 2000. Vol. 62, num. 10, pags. 105006-1-105006-6. ISSN 0556-2821. [consulted: 12 of October of 2026]. Available at: https://hdl.handle.net/2445/12436