
TL;DR
This paper extends the concept of quantomorphisms to metaplectic-c prequantizations, providing a new framework that generalizes classical prequantization and preserves the Poisson algebra structure.
Contribution
It defines metaplectic-c quantomorphisms and infinitesimal quantomorphisms, showing they form a structure isomorphic to the Poisson algebra, thus generalizing classical quantization methods.
Findings
Metaplectic-c quantomorphisms preserve all prequantization structures.
The space of infinitesimal metaplectic-c quantomorphisms is isomorphic to the Poisson algebra.
The definition includes an extra condition due to the complexity of metaplectic-c structures.
Abstract
In the classical Kostant-Souriau prequantization procedure, the Poisson algebra of a symplectic manifold is realized as the space of infinitesimal quantomorphisms of the prequantization circle bundle. Robinson and Rawnsley developed an alternative to the Kostant-Souriau quantization process in which the prequantization circle bundle and metaplectic structure for are replaced by a metaplectic-c prequantization. They proved that metaplectic-c quantization can be applied to a larger class of manifolds than the classical recipe. This paper presents a definition for a metaplectic-c quantomorphism, which is a diffeomorphism of metaplectic-c prequantizations that preserves all of their structures. Since the structure of a metaplectic-c prequantization is more complicated than that of a circle bundle, we find that the definition must include an extra condition that…
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