Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach

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.

21 pages, uses Plain TeX

References in corpus (5)

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• Induced Gauge Fields in the Path Integral
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• Path Integral on Star Graph
• Quantum Caustics for Systems with Quadratic Lagrangians
• Collective Dynamics of Solitons and Inequivalent Quantizations
• Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere
• Path integrals in a multiply-connected configuration space (50 years after)
• Path Integrals on Riemannian Manifolds with Symmetry and Induced Gauge Structure