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Abstract

Abstract (arXiv) Using a quantization of the nonassociative and noncommutative Snyder ϕ4 scalar field theory in a Hermitian realization, we present in this article an evaluation of the momentum-conserving part of the one-loop two-point function in four-dimensional Euclidean space, exact with respect to the noncommutative deformation parameter beta. We prove that the integrals are regularized by the Snyder deformation. These results indicate that the Snyder deformation does partially regularize the UV divergences of the undeformed theory, as it was proposed decades ago. Furthermore, it is observed that different nonassociative ϕ4 products can generate different momentum-conserving integrals. Finally most importantly, a logarithmic infrared divergence emerges in one of these interaction terms. We consider this infrared divergence as UV/IR mixing induced by nonassociativity, since it is associated to the matching UV divergence in the zero-momentum limit and appears in one specific type of nonassociative ϕ4 products. Such UV/IR mixing represents a general quantum feature of nonassociative and noncommutative Snyder ϕ4 scalar field theory at the one-loop level. We also compute and analyze the one-loop three-dimensional Snyder-deformed analogue of the Coleman-Weinberg effective potential, showing that the Snyder deformation may change the behavior of the quantum field theory.