Non-Commutative Complete Mellin Representation for Feynman Amplitudes

Abstract

We extend the complete Mellin (CM) representation of Feynman amplitudes to the non-commutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy of Feynman amplitudes in parameters such as the dimension of space-time. In particular it paves the road for the dimensional renormalization of these theories. This complete Mellin representation also allows the study of asymptotic behavior under rescaling of arbitrary subsets of external invariants of any Feynman amplitude.

14 pages, no figure

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• Non-commutative Renormalization
• Vacuum configurations for renormalizable non-commutative scalar models
• Combinatorial Dyson-Schwinger equations in noncommutative field theory
• Overview of the parametric representation of renormalizable non-commutative field theory
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Noncommutative geometry, gauge theory and renormalization
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• 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
• Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space
• Translation-Invariant Noncommutative Renormalization
• Why Renormalizable NonCommutative Quantum Field Theories?
• Feynman amplitudes in renormalizable non-commutative quantum field theory
• Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0
• Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories
• Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory
• Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory