The project explores the emerging role of methods of non-commutative geometry in string theory and string field theory. The applicant has a background in physics especially string theory and by beating to the quantum groups and non-commutative geometry section at Queen Mary, University of London, will be able to acquire the necessary mathematical tools also.
At the moment, there are several specific points of contact where string theorists have noted the presence of non-commutative geometries such as the Connes-Rieffel non com-mutative torus, but the systematic use of concrete non-commutative geometry methods such as those coming from quantum groups, bicovariant calculi on quantum groups and their homogenous spaces, as well as deeper aspects of the operator theory approach has not been developed in any detail, mainly because of the large gulf in the expertise between string theorists and those who work on such non-commutative methods.
What has been done so far, mainly in the operator K-theory methods applied to string theory h as already proven very interesting at the topological level, with physical interpretations or Monta equivalence etc., but the more (non-commutative) differential aspects are still in early stages. In fact for effective computations and model building physicists need to develop much more concrete tools as well as to understand the physical meaning of the mathematical concepts for Planck scale physics.
Again, the first indications are that non-commutative geometry and specific models of spacetime built using quantum group and other methods will be the way to extract first corrections to classical gravity in quantum gravity models including string ones. As such models show, even though Planck scale effects are fantastically small, their modification to the basic structure of spacetime can accumulate to, in principle, detectable levels in cosmological models.
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