Inequivalent quantizations and holonomy factor from the path-integral approach

Journal Article · Fri Aug 01 00:00:00 EDT 1997 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1997.5696· OSTI ID:542108

Tanimura, S ^[1]; Tsutsui, I ^[2]

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1. Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, Kyoto 606-01 (Japan)
2. Institute for Nuclear Study, University of Tokyo, Midori-cho, Tanashi-shi, Tokyo 188 (Japan)

A path-integral quantization on a homogeneous space G/H is proposed, based on the guiding principle {open_quotes}first lift to G and then project to G/H{close_quotes}. 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 on G/H obtained in various approaches so far. {copyright} 1997 Academic Press, Inc.

• OSTI ID: 542108
• Journal Information: Annals of Physics (New York), Vol. 258, Issue 2; Other Information: PBD: Aug 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTIZATION
FEYNMAN PATH INTEGRAL
LIE GROUPS
PROPAGATOR
WAVE FUNCTIONS
ACTION INTEGRAL
QUANTUM OPERATORS
IRREDUCIBLE REPRESENTATIONS