On Bohr-Sommerfeld bases

On Bohr–Sommerfeld bases

This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr– Sommerfeld (BS) basis. We use the method of Borthwick–Paul–Uribe [BPU], whereby every vector of a BS basis is defined by some halfweighted Legendrian distribution coming from a Bohr–Sommerfeld fibre of a real polarization of the underlying symplectic manifold. The adv...

Bohr-sommerfeld Star Products

We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.

Bohr-Sommerfeld quantization of periodic orbits.

We show, that the canonical invariant part of h̄ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the imp...

Bohr-Sommerfeld conditions for several commuting Hamiltonians

Quantum monodromy and Bohr-Sommerfeld rules

This article is based on a talk given in Dijon for the 2000 summer school “Topological and Geometrical Methods: Applications to Dynamical Systems”. The standard definitions of the monodromy invariant for completely integrable classical systems are reviewed, and the link to the quantum monodromy observed in the joint spectrum of commuting operators is explained. The mathematical treatment relies...