Shifting operators in geometric quantization

Abstract

In a series of papers on Bohr-Sommerfeld-Heisenberg quantization of completely integrable systems we interpreted shifting operators as quantization of functions ${\mathrm{e}}^{\pm i{\theta }_j}$ , where $(I_j,{\theta }_j)$ are action angle coordinates. The aim of this paper is to show how these operators occur in geometric quantization.

This is a revised version. It focuses exclusively on shifting operators in Bohr-Sommerfeld theory of quantization of completely integrable Hamiltonian systems