Worldline Formalism in Snyder Spaces

Abstract

We study the ${\varphi }_{\star }^4$ model for a scalar field in a linearization of the Snyder model, using the methods of the Worldline Formalism. Our main result is a master equation for the 1-loop n-point function. From this we derive the renormalization of the coupling parameters of the theory and observe the appearance of a ${\varphi }^6$ divergent contribution that opens the question of whether this theory is renormalizable or not. Additionally, we observe that some terms in the renormalized action can be interpreted as coming from an effective metric proportional to the square of the field.

13 pages. v2: added eqs. (11) and (12) regarding the effective action, corrected eq. (40)

References in corpus (7)

• Scalar field theory in Snyder space-time: alternatives
• Non-commutative SU(N) gauge theories and asymptotic freedom
• Scalar heat kernel with boundary in the worldline formalism
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• Gravitational form factors and decoupling in 2D
• Relative-locality phenomenology on Snyder spacetime
• Scalar Field with Robin Boundary Conditions in the Worldline Formalism

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• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• 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
• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
• Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy
• Local Neumann semitransparent layers: resummation, pair production and duality
• Graphene in curved Snyder space
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• Doubly special relativity as a non-local quantum field theory
• Covariant dynamics on the energy-momentum space: scalar field theory
• Formal developments in curved momentum space: the quantum field theory roadmap
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Realizations of the Extended Snyder Model