UV/IR Mixing in Nonassociative Snyder phi^4 Theory

Abstract

Using a quantization of the nonassociative and noncommutative Snyder phi^4 scalar field theory in a Hermitian realization, we present in this article analytical formulas for the momentum-conserving part of the one-loop two-point function of this theory in D-, 4-, and 3-dimensional Euclidean spaces, which are exact with respect to the noncommutative deformation parameter beta. We prove that these 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 phi^4 products can generate different momentum-conserving integrals. Finally most importantly, a logarithmic infrared divergence emerges in one of these interaction terms. We then analyze sample momentum nonconserving integral qualitatively and show that it could exhibit IR divergence too. Therefore infrared divergences should exist, in general, in the Snyder phi^4 theory. We consider infrared divergences at the limit p -> 0 as UV-IR mixings induced by nonassociativity, since they are associated to the matching UV divergence in the zero-momentum limit and appear in specific types of nonassociative phi^4 products. We also discuss the extrapolation of the Snyder deformation parameter beta to negative values as well as certain general properties of one-loop quantum corrections in Snyder phi^4 theory at the zero-momentum limit.

14 pages, 3 figures, version to be published in Phys. Rev. D

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• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Seiberg-Witten map Invariant Scatterings
• Vacuum energy from noncommutative models
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Revisiting NCQED and scattering amplitudes
• Bounds on the scale of noncommutativity from mono photon production in ATLAS Runs -1 and -2 experiments at LHC energies
• UV/IR mixing in Noncommutative SU(N) Yang-Mills theory
• On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes