Parametric representation of noncommutative field theory - Gurǎu, Rǎzvan; Rivasseau, Vincent (Communications in mathematical physics, 2007)
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 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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