XXXII Workshop on Geometric Methods in Physics 30.06-6.07.2013

William Kirwin

Complex-time flows in geometric quantization

Using ideas of Thiemann, the adapted complex structure on a tubular neighborhood of a real-analytic Riemannian manifold in its tangent bundle can be understood as the ``time-i'' geodesic flow. On the tangent bundle of a compact Lie group, the geometric quantization of this flow composed with the Schroedinger quantization of the associated Hamiltonian is Hall's coherent state transform (CST), a unitary isomorphism relating square-integrable functions on the group to certain holomorphic functions on the complexification. In this talk, I will explain these ideas, and how they may be generalized to yield an infinite-dimensional family of ``complex-time'' flows, each of which generates a generalized CST.

Event sponsored by:
Belgian Science Policy Office     PAI          University
of Bialystok
University of Bialystok

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