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

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

2002-01-28

arxiv.org/abs/quant-ph/0201129v2

J. Phys. A: Math. Gen. 35, 5599 (2002)

Physics

Quantum Physics

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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