arXiv subjects
Publications and source records attributed to Razvan Gurau.
We prove that the beta function of the Grosse-Wulkenhaar model including a magnetic field vanishes at all order of perturbations. We compute the renormalization group flow of the relevant dynamic parameters and find a non-Gaussian infrared fixed point. Some consequences of these results are discussed.
Non commutative quantum field theory is a possible candidate for the quantization of gravity. In our thesis we study in detail the $ϕ4$ model on the Moyal plane with an harmonic potential. Introduced by Grosse and Wulkenhaar, this model exhibits the Langmann-Szabo duality not only for the vertex but also for the propagator. We have obtained several results concerning this model. We have proved the renormalisability of this theory at all orders in the position space. We have introduced the parametric and Complete Mellin representation for the model. Furthermore we have proved that the coupling constant has a bounded flow at all orders in perturbation theory. Finally we have achieved the dimensional regularization and renormalization of the model. Further possible studies include the study of gauge theory on the Moyal plane and there possible applications for the quantization of gravity. The connections with string theory and loop quantum gravity should also be investigated.
We present an overview of the different renormalization proofs of the non commutative $ϕ_4^{\star 4}$ model. This paper is a contribution to the MemPhys project.
We show that the simplest non commutative renormalizable field theory, the $ϕ^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe to all orders in perturbation theory
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 {\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.
In this paper we provide a new proof that the Grosse-Wulkenhaar non-commutative scalar Phi^4_4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).