Dynamical Invariance of a New Metaplectic-c Quantization Condition

TL;DR

This paper introduces a new geometric condition for quantized energy levels in metaplectic-c quantization, which depends solely on the level set geometry, enhancing previous methods by Robinson.

Contribution

It proposes a dynamical invariance condition for metaplectic-c quantization levels that depends only on the geometry of the level set, not on the specific dynamics.

Findings

The condition is evaluated on a bundle over the level set of H at E.

The result depends only on the geometry of the level set.

It improves earlier constructions by Robinson.

Abstract

Metaplectic-c quantization was developed by Robinson and Rawnsley as an alternative to the classical Kostant-Souriau quantization procedure with half-form correction. Given a metaplectic-c quantizable symplectic manifold M and a smooth function H on M, this paper proposes a condition under which E, a regular value of H, is a quantized energy level for the system. The condition is evaluated on a bundle over the level set of H at E. We prove that the result depends only on the geometry of the level set, and not on the dynamics of a particular function, improving on an earlier construction by Robinson.