S D Bartlett et al 2002 J. Phys. A: Math. Gen. 35 5625 doi:10.1088/0305-4470/35/27/307
Vector coherent state representations, induced representations and geometric quantization: II. Vector coherent state representations
S D Bartlett1,2, D J Rowe1 and J Repka3
Show affiliationsIt is shown here and in the preceding paper (Bartlett S D, Rowe D J and Repka J 2002 J. Phys. A: Math. Gen. 35) that vector coherent state theory, the theory of induced representations and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of generalizing its counterparts. In this paper, we focus on the construction of quantum models for algebraic systems with intrinsic degrees of freedom. Semi-classical partial quantizations, for which only the intrinsic degrees of freedom are quantized, arise naturally out of this construction. The quantization of the SU(3) and rigid rotor models are considered as examples.
- 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)
81Q20 Semiclassical techniques including WKB and Maslov methods
- 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: II. Vector coherent state representations
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