Classical Mechanics and geometric Quantization on an Infinite Dimensional Disc and Grassmannian

TL;DR

This paper explores classical mechanics on infinite-dimensional geometric spaces like the Grassmannian and Disc, applying geometric quantization methods and examining their relation to flat symplectic spaces.

Contribution

It introduces geometric quantization techniques for infinite-dimensional Grassmannian and Disc models, linking them to flat symplectic spaces.

Findings

Application of geometric quantization to infinite-dimensional spaces

Establishment of relations to flat symplectic spaces

Insights into classical mechanics on infinite-dimensional manifolds

Abstract

We discuss the classical mechanics on the Grassmannian and the Disc modeled on the ideal L^(2,\infty)(H). We apply methods of geometric quantization to these systems. Their relation to a flat symplectic space is also discussed.