In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that this model does not suffer from the UV/IR mixing and we establish its renormalizability to all orders in perturbation theory.
We extend the complete Mellin (CM) representation of Feynman amplitudes to the non-commutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy of Feynman amplitudes in parameters such as the dimension of space-time. In particular it paves the road for the dimensional renormalization of these theories.… (More)
We investigate the relationship between the universal topological polyno-mials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first paper we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are… (More)
We extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call " critical " , because their power counting is definitely more difficult to obtain.This class of theories is important since it includes gauge theories, which should be relevant for the quantum Hall effect. Quantum field… (More)
We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired in the Lie (super)algebra structure, is explicitly applied to the particular case of (graded) contractions of the orthogonal real algebra so(N + 1). In this way we show that " classical " contraction… (More)
We contruct here the Hopf algebra structure underlying the process of renormal-ization of non-commutative quantum eld theory.
Recently, a new type of renormalizable φ ⋆4 4 scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a a/(θ 2 p 2) term. We calculate here the β and γ functions at one-loop level for this model. The coupling constant β λ function is proved to have the same behavior as the one… (More)
We make here a short overview of the recent developments regarding translation-invariant models on the noncommutative Moyal space. A scalar model was first proposed and proved renormalizable. Its one-loop renormalization group flow and parametric representation were calculated. Furthermore, a mechanism to take its commutative limit was recently given.… (More)
We introduce here the Hopf algebra structure describing the noncommutative renormal-ization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles B γ + which allows us to write down the combinatorial Dyson-Schwinger equations for noncommutative quantum field theory. One-and two-loops examples are explicitly… (More)
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with quantum field theory, from a combinatorial point of view. A grafting operator is introduced allowing for the equivalent of… (More)