Semi-Classical Properties of Geometric Quantization with Metaplectic Correction

Semi-Classical Quantization of the Many-Anyon System

We discuss the problem of N anyons in harmonic well, and derive the semi-classical energy spectrum as an exactly solvable limit of the many-anyon Hamiltonian. The relevance of our result to the solution of the anyon-gas model is discussed. PACS numbers: 03.65.Ca, 03.65.Sq, 05.30.-d DFPD 92/TH/26 May 1992 Bitnet address: [email protected] 1

Geometric Optics and Instability for Semi-classical Schrödinger Equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the p...

Weyl Quantization from Geometric Quantization

In [23] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Quantization of Classical Curves

We discuss the relation between quantum curves (defined as solutions of equation [P,Q] = ~, where P,Q are ordinary differential operators) and classical curves. We illustrate this relation for the case of quantum curve that corresponds to the (p, q)minimal model coupled to 2D gravity.