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

TL;DR

This paper develops a translation-invariant noncommutative Yukawa theory in four dimensions, deriving Feynman rules and calculating one-loop quantum corrections to propagators and vertices.

Contribution

It introduces a new translation-invariant noncommutative fermion model and applies it to Yukawa interactions, extending previous scalar-only models.

Findings

Explicit one-loop quantum corrections calculated

Feynman rules derived for the noncommutative Yukawa theory

Model maintains translation invariance in noncommutative space

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 Phi4 theory introduced by R. Gurau et al. We combine our model with the 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 to the propagators and vertices.