Obiettivo Non-commutative geometry was proposed earlier than renormalization as a possible way to eliminate ultraviolet divergences in quantum field theories. On the other hand quantum field theories on non-commutative spaces are generally unknown beyond the one-lo op approximation. A gauge-covariant, chiral-invariant regularization of gauge theories can be achieved by quantizing the underlying space-time manifold thereby replacing it by a non-commutative matrix model or a "fuzzy manifold''. Indeed if the underlying space-time manifold can be treated as a phase space one can quantize it in the usual way with a parameter theta assuming the role of hbar. Naturally the emergent quantum space is fuzzy with non-commuting coordinates and a finite number of degrees of freedom and as a consequence it is ultraviolet finite. The continuum limit is the semi-classical theta goes to zero limit. These are essentially matrix models. The advantage of this regulator compared to ordinary lattice prescription is that discretization by quantization is remarkably successful in preserving symmetries and topological features and altogether avoiding the fermion-doubling problem. As it turns out fuzzy spaces can also be used to regularize infinite dimensional non-commutative spaces such as Moya l-Weyl spaces. The main focus of this proposal is the construction of a new non-perturbative method for chiral gauge theories based on the fuzzy tw-spheres and their Cartesian products.More precisely we will use Monte Carlo numerical simulations to:a) determine the phase structure of 2-dimensional non-commutative fuzzy Yang-Mills theory , andb) to solve the non-commutative fuzzy Schwinger model.This will provide a crucial step towards understanding chiral gauge theories on infinite dimensional non-commutative Moyal-Weyl spaces. But it will also lay the foundation for the study of ordinary QCD in two and four dimensions using fuzzy approximations. Campo scientifico natural sciencesphysical sciencestheoretical physicsparticle physicsfermionsnatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesmathematicspure mathematicsgeometry Programma(i) 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 Argomento(i) MOBILITY-2.3 - Marie Curie Incoming International Fellowships (IIF) Invito a presentare proposte FP6-2004-MOBILITY-7 Vedi altri progetti per questo bando Meccanismo di finanziamento IIF - Marie Curie actions-Incoming International Fellowships Coordinatore HUMBOLDT-UNIVERSITÄT ZU BERLIN Contributo UE Nessun dato Indirizzo Unter den Linden 6 BERLIN Germania Mostra sulla mappa Collegamenti Sito web Opens in new window Costo totale Nessun dato