School of Mathematics & Statistics

Rieffel type quantisation of symplectic manifolds

Ryszard Nest (University of Copenhagen)

Thursday 15th October 15:00-16:00
Maths 311B

Abstract

Standard physics approach to quantisation of symplectic manifolds, geometric quantisation, puts severe restrictioins on the cohomology class of the symplectic form. On the other hand there is a big class of examples of both quantum mechanical and mathematical origin, where this condition is not satisfied. The simplest class consists of complex curves of genus of at least one. The results in this case can be generalised to arbitrary symplectic manifolds with the aspherical class of the symplectic form. On the other hand, the index formulas from formal deformation theory indicate that there should exist a construction of quantisation which also covers these cases.

We will explain the general idea behind the existing constructions and indicate a possible ways of dealing with the case of the two-dimansional sphere.

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