Objective This project aims at studying the renormalization of non-commutative field theories in a systematic way. Recently H. Grosse and R. Wulkenhaar proved that one can cure the IR/UV mixing of such theories by adding a new term in the Lagrangian. For the non-com mutative phi**4 theory, this harmonic potential term makes the theory renormalizable to all orders.An other model is renormalizable thanks to a similar procedure: the Gross-Neveu model on the Moyal plane. Nevertheless there is currently no way of computing the missing counterterm for other non-commutative spaces. The first part of the project will be devoted to the study of the space dependency of the renormalization procedure.We will consider different quartically interacting models (as phi**4 or Gross-Neveu) on non-commutative spaces and find the appropriate counterterms. The second part will concern the regularisation properties of non-commutative spaces. The non-commutative phi**4 model exhibits bounded renormalization group flow. In contrast its commutative counterpart has unbounded flow.The generality of such a feature will be studied. We also want to probe non-perturbative aspects of non-commutative field theories. We will use constructive techniques to define non-perturbatively such theories. Finally we want to examine the link between String theory and these new classes of non-commutative field theories. Fields of science natural sciencesphysical sciencestheoretical physicsparticle physicsparticle acceleratornatural sciencesphysical sciencesrelativistic mechanicsnatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometry Keywords Non Non-commutative Geometry Renormalization Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Topic(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Call for proposal FP6-2005-MOBILITY-5 See other projects for this call Funding Scheme EIF - Marie Curie actions-Intra-European Fellowships Coordinator UNIVERSITÄT WIEN EU contribution No data Address Dr. Karl Lueger-Ring 1 WIEN Austria See on map Links Website Opens in new window Total cost No data