Parametric Representation of Noncommutative Field Theory

2006/06/09 by Razvan Gurău, Razvan Gurau, Vincent Rivasseau · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s00220-007-0215-5

published as Commun.Math.Phys.272:811-835,2007 · 31 pages,10 figures

arxiv created 2006/06/09 · openalex publication_date 2007/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable ϕ⁴₄ quantum field theory on the Moyal non commutative \mathbb R⁴ 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.

Citations

• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Renormalization of the Orientable Non-commutative Gross–Neveu Model

Cited by

• Parametric Representation of “Covariant” Noncommutative QFT Models
• EXISTENCE OF ASYMPTOTIC EXPANSIONS IN NONCOMMUTATIVE QUANTUM FIELD THEORIES
• Vanishing β-function for Grosse–Wulkenhaar model in a magnetic field