2012/07/05 by Richard Cushman, Cushman, Richard, Jędrzej Śniatycki +1
Engineering · Mathematics · Physics and Astronomy · #81S10 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Photonic and Optical Devices #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1207.1302
openalex publication_date 2012/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal basis in the space of quantum states, but also give a lattice structure to this basis. This permits the definition of appropriate shifting operators. As examples, we discuss the 1-dimensional harmonic oscillator and the coadjoint orbits of the rotation group.