20 06 Bohr - Sommerfeld Star Products

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.

Ju n 20 06 Universal Maslov class of Bohr - Sommerfeld lagrangian embedding to pseudo - Einstein manifold

Bohr-Sommerfeld Rules to All Orders

The goal of this paper is to give a rather simple algorithm which computes the Bohr-Sommerfeld quantization rules to all orders in the semi-classical parameter h for a semi-classical Hamiltonian Ĥ on the real line. The formula gives the highorder terms in the expansion in powers of h of the semi-classical action using only integrals on the energy curves of quantities which are locally computabl...

The Wave Function of a Collapsing Star and Quantization Conditions

A very simple minisuperspace describing the Oppenheimer-Snyder collapsing star is found. The semiclassical wave function of that model turn out to describe a bound state. For fixed initial radius of the collapsing star, the corresponding Bohr-Sommerfeld quantization condition implies mass quantization. An extension of this model, and some consequences, are considered. This work is supported by ...

S’darboux Coordinates and Wkb Approximations in Deformation Quantization

We introduce a method for calculating the joint spectra of functions which comprise a quantum integrable system under a deformation quantization star product. The main result involves a construction by formal power series in ~ of s’Darboux coordinates, a concept we introduce for the star product analogue of Darboux normal coordinates. We will find that underlying the quantum integrable system i...