Abstract
We consider the noncommutative space ℝ 3 θ , a deformation of ℝ 3 for which the star product is closed for the trace functional. We study one-loop IR and UV properties of the 2-point function for real and complex noncommutative scalar field theories with quartic interactions and Laplacian on ℝ 3 as kinetic operator. We find that the 2-point functions for these noncommutative scalar field theories have no IR singularities in the external momenta, indicating the absence of UV/IR mixing. We also find that the 2-point functions are UV finite with the deformation parameter θ playing the role of a natural UV cut-off. The possible origin of the absence of UV/IR mixing in noncommutative scalar field theories on ℝ 3 θ as well as on ℝ 3 λ , another deformation of ℝ 3, is discussed.
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Jurić, T., Poulain, T. & Wallet, JC. Closed star product on noncommutative ℝ 3 and scalar field dynamics. J. High Energ. Phys. 2016, 146 (2016). https://doi.org/10.1007/JHEP05(2016)146
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DOI: https://doi.org/10.1007/JHEP05(2016)146