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

Bartlett, Stephen D.; Rowe, David J.; Repka, Joe

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

Authors

Bartlett, Stephen D.

Rowe, David J.

Repka, Joe

Description

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