2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189809In 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.31 pages,10 figuresMathematical PhysicsHigh Energy Physics - Theorytext