Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-08-06
Annals Phys. 237 (1995) 269-321
Physics
High Energy Physics
High Energy Physics - Theory
64 pages, plain TeX, DIAS-STP-93-14
Scientific paper
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.
McMullan David
Tsutsui Izumi
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