Invariance of Polarization Induced by Symplectomorphisms

TL;DR

This paper investigates how symplectomorphisms act on real singular polarizations in symplectic manifolds and demonstrates that, under certain conditions, this action preserves the quantization process associated with a prequantum line bundle.

Contribution

It introduces an action of symplectomorphisms on polarizations and proves its invariance of quantization under specific topological conditions.

Findings

Symplectomorphisms act on real singular polarizations.

Quantization is preserved under the symplectomorphism action.

Topological conditions ensure invariance of quantization.

Abstract

In this paper we define an action by the symplectomorphisms on a symplectic manifold on the space of real singular polarizations. It is then shown that under some topological conditions, this action preserves quantization by a fixed prequantum line bundle.