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Journals and Conferences
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 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.
The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace of a operator expressed as a function of the creation and annihilation operators.
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)
Communicated by Martin Schlichenmaier Abstract. We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired by 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… (More)
We contruct here the Hopf algebra structure underlying the process of renormalization of non-commutative quantum eld theory.
Recently, a new type of renormalizable φ 4 scalar model on the Moyal space was proved to be perturbatively renormalizable. It is translation-invariant and introduces in the action a a/(θp) term. We calculate here the β and γ functions at one-loop level for this model. The coupling constant βλ function is proved to have the same behavior as the one of the φ… (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)
We introduce here the Hopf algebra structure describing the noncommutative renormalization 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 DysonSchwinger equations for noncommutative quantum field theory. Oneand two-loops examples are explicitly… (More)