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Parametric Representation of Noncommutative Field Theory

Razvan Gurau·Vincent Rivasseau
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Abstract

In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable $ϕ^4_4$ 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.

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Razvan Gurau, Vincent Rivasseau. 2006-06-09. Parametric Representation of Noncommutative Field Theory. https://doi.org/10.1007/s00220-007-0215-5

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