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

Physics – Quantum Physics

Scientific paper

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29 pages, part 1 of two papers, published version

Scientific paper

10.1088/0305-4470/35/27/306

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.

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