Closed star product on noncommutative ^sup 3^ and scalar field dynamics

Abstract We consider the noncommutative space [theta] 3 , a deformation of 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 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 [theta] 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 [theta] 3 as well as on [lambda] 3 , another deformation of 3, is discussed.