Generalization of Integrality Condition of Prequantization to Phase Space with Boundaries

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.