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

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.

29 pages, part 1 of two papers, published version

References in corpus (3)

• Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations
• On Quantizing $T^{\ast }{S}^1$
• Vector Coherent State Realization of Representations of the Affine Lie Algebra $\widehat{sl}(2)$

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