Parametric Representation of Noncommutative Field Theory

Abstract

In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable ${\varphi }_4^4$ quantum field theory on the Moyal non commutative ${\mathbb{R}}^4$ space. This representation involves new {\it hyperbolic} polynomials which are the non-commutative analogs of the usual "Kirchoff" or "Symanzik" polynomials of commutative field theory, but contain richer topological information.

31 pages,10 figures

References in corpus (2)

• From Physics to Number Theory via Noncommutative Geometry, Part II: Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory
• Renormalization of the Orientable Non-commutative Gross-Neveu Model

Cited by in corpus (16)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• A translation-invariant renormalizable non-commutative scalar model
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Overview of the parametric representation of renormalizable non-commutative field theory
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of "critical" noncommutative QFT models
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Why Renormalizable NonCommutative Quantum Field Theories?
• Feynman amplitudes in renormalizable non-commutative quantum field theory
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories
• Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory