Quantization of systems with a general phase space equipped with a Riemannian metric

Abstract

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 structure. Using techniques from differential geometry, and especially exploiting the Dirac operator, we are able to offer a fully geometric quantization procedure for a wide class of symmetry free phase spaces. Our procedure leads to the conventional results in cases where the phase space is a symmetric space for which alternative quantization techniques suffice.