OPERATOR ORDERING PROBLEM AND COORDINATE-FREE NATURE OF GEOMETRIC-QUANTIZATION

Operator ordering problem in geometric quantization is investigated. W hile the quantum operator for p(2)f(q) given 'by geometric quantizatio n is found to be ordered via the rule invariant under general coordina te transformations, it is shown that the quantum operators for p(n)f(p ) when n > 2 cannot be well-defined by geometric quantization. This is considered as a natural consequence of the coordinate-free nature of geometric quantization and the Van Hove's theorem.