Gauging and Symplectic Blowing Up in Nonlinear Sigma Models: I. Point Singularities
نویسنده
چکیده
In this paper a two dimensional non-linear sigma model with a general symplectic manifold with isometry as target space is used to study symplectic blowing up of a point singularity on the zero level set of the moment map associated with a quasifree Hamiltonian action. We discuss in general the relation between symplectic reduction and gauging of the symplectic isometries of the sigma model action. In the case of singular reduction, gauging has the same effect as blowing up the singular point by a small amount. Using the exponential mapping of the underlying metric, we are able to construct symplectic diffeomorphisms needed to glue the blow-up to the global reduced space which is regular, thus providing a transition from one symplectic sigma model to another one free of singularities. Alexander von Humboldt fellow, on leave from Zhejiang University, Institute of Modern Physics, Hangzhou, China
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