Objective
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 , and
b) 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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences physical sciences theoretical physics particle physics fermions
- natural sciences physical sciences quantum physics quantum field theory
- natural sciences mathematics pure mathematics geometry
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-7
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
IIF - Marie Curie actions-Incoming International Fellowships
Coordinator
BERLIN
Germany
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