Communications in Mathematical Physics

, Volume 272, Issue 3, pp 811–835 | Cite as

Parametric Representation of Noncommutative Field Theory

  • Razvan Gurau
  • Vincent Rivasseau


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


Parametric Representation Dual Graph Power Counting Ribbon Graph External Argument 
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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris XIOrsay CedexFrance

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