ON THE EMERGENCE OF GAUGE STRUCTURES AND GENERALIZED SPIN WHEN QUANTIZING ON A COSET SPACE

It has been known for some time that there are many inequivalent quantizations possible when the configuration space of a system is a coset space G/H. Viewing this classical system as a constrained system on the group G, we show that these inequivalent quantizations can be recovered from a generalization of Dirac's approach to the quantization of such a constrained system within which the classical first class constraints (generating the H-action on G) are allowed to become anomalous (second class) when quantizing. The resulting quantum theories are characterized by the emergence of a Yang-Mills connection, with quantized couplings, and new ''spin'' degrees of freedom. Various applications of this procedure are presented in detail: including a new account of how spin can be described within a path-integral formalism, and how on S-4 chiral spin degrees of freedom emerge, coupled to a BPST instanton. (C) 1995 Academic Press, Inc.