Shifting operators in geometric quantization

Richard Cushman; Jedrzej Sniatycki

Shifting operators in geometric quantization

Symplectic Geometry 2020-01-13 v3

Authors: Richard Cushman , Jedrzej Sniatycki

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.

Keywords

operator theory pseudodifferential operators

Cite

@article{arxiv.1808.04002,
  title  = {Shifting operators in geometric quantization},
  author = {Richard Cushman and Jedrzej Sniatycki},
  journal= {arXiv preprint arXiv:1808.04002},
  year   = {2020}
}

Comments

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

Shifting operators in geometric quantization

Abstract

Keywords

Cite

Comments

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