Universität zu Köln

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

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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:	Creators Email ORCID ORCID Put Code Kirwin, William D. UNSPECIFIED UNSPECIFIED UNSPECIFIED Mourao, Jose M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Nunes, Joao P. UNSPECIFIED UNSPECIFIED UNSPECIFIED
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
Uncontrolled Keywords:	Keywords Language MONGE-AMPERE EQUATION; RIEMANNIAN-MANIFOLDS; HIGHER ASYMPTOTICS; GRAUERT TUBES; LIE-GROUPS; REDUCTION; UNITARITY; COMMUTES; BUNDLE Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47403