S D Bartlett et al 2002 J. Phys. A: Math. Gen. 35 5599 doi:10.1088/0305-4470/35/27/306
Vector coherent state representations, induced representations and geometric quantization: I. Scalar coherent state representations
S D Bartlett1,2, D J Rowe1 and J Repka3
Show affiliationsCoherent 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
- MSC
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81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
- Subjects
- Dates
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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
S D Bartlett et al 2002 J. Phys. A: Math. Gen. 35 5599
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