VCS representations, induced representations and geometric quantization I

doi:10.1088/0305-4470/35/27/306

Vector coherent state representations, induced representations and geometric quantization: I. Scalar coherent state representations

S D Bartlett et al 2002 J. Phys. A: Math. Gen. 35 5599-5623 doi: 10.1088/0305-4470/35/27/306

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S D Bartlett^1,2, D J Rowe¹ and J Repka³
¹ Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
² Department of Physics, Macquarie University, Sydney, New South Wales 2109, Australia
³ Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
E-mail: stephen.bartlett@mq.edu.au

Abstract. Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization, (ii) induced unitary representations corresponding to prequantization and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.

PACS numbers: 03.65.Fd, 02.20.−a, 04.60.Ds

Print publication: Issue 27 (12 July 2002)
Received 31 January 2002, in final form 13 May 2002
Published 28 June 2002

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Vector coherent state representations, induced representations and geometric quantization: I. Scalar coherent state representations

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