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We elaborate in this paper a translation-invariant model for fermions in4-dimensional noncommutative Euclidean space. The construction is done on thebasis of the renormalizable noncommutative translation-invariant Phi4 theoryintroduced by R. Gurau et al. We combine our model with the scalar model, inorder to study the noncommutative pseudo-scalar Yukawa theory. After we derivethe Feynman rules of the theory, we perform an explicit calculation of thequantum corrections at one loop level to the propagators and vertices.

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