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

摘要

Coherent state theory is shown to reproduce three categories ofrepresentations 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 bychoice of a polarization. These representations establish an intimate relationbetween coherent state theory and geometric quantization in the context ofinduced representations.