Geometric quantization of weak-Hamiltonian functions

TL;DR

This paper extends geometric quantization to integrable big-isotropic structures, generalizing cohomology conditions and polarization concepts to accommodate weak-Hamiltonian functions.

Contribution

It introduces a novel framework for quantizing weak-Hamiltonian functions within integrable big-isotropic structures, expanding the scope of geometric quantization.

Findings

Generalized cohomology integrality condition

Described geometric structures on principal circle bundles

Extended the notion of polarization for these structures

Abstract

The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the corresponding principal circle bundle and we extend the notion of a polarization.