INEQUIVALENT QUANTIZATIONS AND HOLONOMY FACTOR FROM THE PATH-INTEGRALAPPROACH

A path-integral quantization on a homogeneous space G/H is proposed, b ased on the guiding principle ''first lift to G and then project to G/ 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 held) found earlier by algebra ic approaches. We also prove that the resulting matrix-valued path-int egral is physically equivalent to the scalar-valued path-integral deri ved in the Dirac approach, and thereby we present a unified viewpoint to discuss the basic features of quantizing on G/H obtained in various approaches so far. (C) 1997 Academic Press.