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

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 ${\phi }^4$ 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. (paper)