Nonassociative Snyder phi4 Quantum Field Theory

Abstract

In this article we define and quantize a truncated form of the nonassociative and noncommutative Snyder phi^4 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 beta, 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 beta^1 order except for the special choice of free parameters s_1=-s_2. We expect effects from nonassociativity on the correlation functions at beta^1 order, but these are cancelled due to the average over permutations.

13 pages, 6 figures. Version to be published in Phys.Rev.D

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Cited by in corpus (18)

• Worldline Formalism in Snyder Spaces
• Associative realizations of the extended Snyder model
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Heisenberg doubles for Snyder type models
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Casimir effect in Snyder Space
• Noncommutative Yang model and its generalizations
• Seiberg-Witten map Invariant Scatterings
• Graphene in curved Snyder space
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• Twist for Snyder space
• Doubly special relativity as a non-local quantum field theory
• Revisiting NCQED and scattering amplitudes
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries