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arXiv · hep-th/9609089

Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach

Shogo Tanimura·Izumi Tsutsui
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Abstract

A path-integral quantization on a homogeneous space G/H is proposed based 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 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 present a unified viewpoint to discuss the basic features of quantizing on $G/H$ obtained in various approaches so far.

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Shogo Tanimura, Izumi Tsutsui. 1996-09-11. Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach. https://doi.org/10.1006/aphy.1997.5696

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