Gauge invariant quantization on Riemannian manifolds

Abstract

For every pointwise polynomial function on each fiber of the cotangent bundle of a Riemannian manifold M M , a family of differential operators is given, which acts on the space of smooth sections of a vector bundle on M M . Such a correspondence may be considered as a rule to quantize classical systems moving in a Riemannian manifold or in a gauge field. Some applications of our construction are also given in this paper.