Generalization of Integrality Condition of Prequantization to Phase Space with Boundaries

TL;DR

This paper extends Weil's integrality condition for prequantization line bundles to phase spaces with boundaries, providing proofs and linking it to topological indices of singular points.

Contribution

It generalizes the integrality condition to bounded phase spaces and establishes a topological interpretation involving indices of singular points.

Findings

Necessity and sufficiency proofs provided

Connection between integrality condition and topological indices established

Extension to phase spaces with boundaries achieved

Abstract

The Weil's integrality condition of prequantization line bundle is generalized to phase space with boundaries. The proofs of both necessity and sufficiency are given. It is pointed out via the method of topological current that Weil's integrality condition is closely connected with the summation of index of isolated singular points of sections of prequantization line bundle.