One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory

Abstract

We elaborate in this paper a translation-invariant model for fermions in 4-dimensional noncommutative Euclidean space. The construction is done on the basis of the renormalizable noncommutative translation-invariant theory introduced by Gurau et al. 2009 Commun. Math. Phys. 287 275–90. We combine our model with a scalar model, in order to study the noncommutative pseudo-scalar Yukawa theory. After we derive the Feynman rules of the theory, we perform an explicit calculation of the quantum corrections at one loop level for the propagators and vertices.