Kirwin, William D., Mourao, Jose M. and Nunes, Joao P. (2013). Complex time evolution in geometric quantization and generalized coherent state transforms. J. Funct. Anal., 265 (8). S. 1460 - 1494. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-0783
Full text not available from this repository.Abstract
For the cotangent bundle T* K of a compact Lie group K, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space L-2(K) under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state transform (CST), which is a unitary isomorphism between L-2(K) and a certain weighted L-2-space of holomorphic functions. For a particular set of choices, we show that this isomorphism is naturally decomposed as a product of a Heisenberg-type evolution (for complex time -tau) within L-2(K), followed by a polarization-changing geometric-quantization evolution (for complex time +tau). In this case, our construction yields the usual generalized Segal-Bargmann transform of Hall. We show that the infinite-dimensional family of Hamiltonian flows can also be understood in terms of Thiemann's complexifier method (which generalizes the construction of adapted complex structures). (C) 2013 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-474032 | ||||||||||||||||
DOI: | 10.1016/j.jfa.2013.06.021 | ||||||||||||||||
Journal or Publication Title: | J. Funct. Anal. | ||||||||||||||||
Volume: | 265 | ||||||||||||||||
Number: | 8 | ||||||||||||||||
Page Range: | S. 1460 - 1494 | ||||||||||||||||
Date: | 2013 | ||||||||||||||||
Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | ||||||||||||||||
Place of Publication: | SAN DIEGO | ||||||||||||||||
ISSN: | 1096-0783 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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URI: | http://kups.ub.uni-koeln.de/id/eprint/47403 |
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