Abstract
A path-integral quantization on a homogeneous spaceG/His proposed, based on the guiding principle “first lift toGand then project toG/H”. It is then shown that this principle gives a simple procedure to obtain the inequivalent quantizations (superselection sectors), along with the holonomy factor (induced gauge field) found earlier by algebraic approaches. We also prove that the resulting matrix-valued path-integral is physically equivalent to the scalar-valued path-integral derived in the Dirac approach, and thereby we present a unified viewpoint to discuss the basic features of quantizing onG/Hobtained in various approaches so far.
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