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 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 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)
Renormalizable φ ⋆4 4 models on Moyal space have been obtained by modifying the com-mutative propagator. But these models have a divergent " naive " commutative limit. We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model. The mechanism relies on the analysis of the uv/ir mixing in general… (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)
Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expansion in N , the size of the tensor, of a… (More)
We consider here the Feynman amplitudes of renormalizable non-commutative quantum field theory models. Different representations (the parametric and the Mellin one) are presented. The latter further allows the proof of meromorphy of a amplitude in the space-time dimension.