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

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Cited by in corpus (40)

• Colored Tensor Models - a Review
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• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• On the periods of some Feynman integrals
• Topological Graph Polynomials in Colored Group Field Theory
• Non-commutative Renormalization
• Linearized Group Field Theory and Power Counting Theorems
• A translation-invariant renormalizable non-commutative scalar model
• The Tensor Track, III
• Vacuum configurations for renormalizable non-commutative scalar models
• Multi-orientable Group Field Theory
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Quantum Corrections in the Group Field Theory Formulation of the EPRL/FK Models
• Combinatorial Dyson-Schwinger equations in noncommutative field theory
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Generalization of the Bollobás-Riordan polynomial for tensor graphs
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• 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
• Noncommutative geometry, gauge theory and renormalization
• Spectral geometry of the Moyal plane with harmonic propagation
• Tree Quantum Field Theory
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Why Renormalizable NonCommutative Quantum Field Theories?
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Feynman amplitudes in renormalizable non-commutative quantum field theory
• The Ponzano-Regge model and parametric representation
• A multidimensional generalization of Symanzik polynomials
• Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories
• A numerical approach to harmonic non-commutative spectral field theory
• The renormalization of non commutative ϕ_4^{\star 4}
• Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory
• First numerical approach to a Grosse-Wulkenhaar model