QUANTIZATION OF SYSTEMS WITH A GENERAL PHASE-SPACE EQUIPPED WITH A RIEMANNIAN METRIC

Quantization on phase spaces of general geometry devoid of any special symmetry properties is discussed on the basis of phase spaces endowed with a symplectic structure, a Riemannian geometry, and a Spin(c) str ucture. Using techniques from differential geometry, and especially ex ploiting the Dirac operator, we are able to offer a fully geometric qu antization procedure for a wide class of symmetry free phase spaces. O ur procedure leads to the conventional results in cases where the phas e space is a symmetric space for which alternative quantization techni ques suffice.