Nonassociative Snyder φ4 quantum field theory

Meljanac, Stjepan;Mignemi, Salvatore;Trampetic, Josip;You, Jiangyang

2017-01-01

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Abstract

In this article, we define and quantize a truncated form of the nonassociative and noncommutative Snyder φ4 field theory using the functional method in momentum space. More precisely, the action is approximated by expanding up to the linear order in the Snyder deformation parameter β, producing an effective model on commutative spacetime for the computation of the two-, four- and six-point functions. The two- and four-point functions at one loop have the same structure as at the tree level, with UV divergences faster than in the commutative theory. The same behavior appears in the six-point function, with a logarithmic UV divergence and renders the theory unrenormalizable at β1 order except for the special choice of free parameters s1=-s2. We expect effects from nonassociativity on the correlation functions at β1 order, but these are cancelled due to the average over permutations.