Shifting operators in geometric quantization

2018/08/12 by Cushman, Richard, Sniatycki, Jedrzej
#81S10 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1808.04002

Abstract

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

Related

• Bohr-Sommerfeld-Heisenberg Theory in Geometric Quantization
• On Bohr-Sommerfeld-Heisenberg Quantization
• Holonomic control operators in quantum completely integrable Hamiltonian systems
• Remarks on the geometric quantization of a class of harmonic oscillator type potentials
• Geometric Quantization