BPST instanton and Spin from inequivalent quantizations

Abstract

We present a simple alternative to Mackey's account of the (infinite) inequivalent quantizations possible on a coset space G/H. Our reformulation is based on the reduction $\mathrm{G}\to G/H$ and employs a generalized form of Dirac's approach to the quantization of constrained systems. When applied to the four-sphere $S^4\simeq \mathrm{Spin}(5)/Spin(4)$, the inequivalent quantizations induce relativistic spin and a background BPST instanton; thus they might provide a natural account of both of these physical entities.

11 pages, plain TeX, PLY-MS-93-04, DIAS-STP-93-21 (This version should now TeX)

Cited by in corpus (8)

• The canonical connection in quantum mechanics
• Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach
• Quantum Mechanically Induced Hopf Term in the O(3) Nonlinear Sigma Model
• Compositeness Condition for Dynamically Induced Gauge Theories
• Quantum Mechanics on S^n and Meron Solution
• Hopf Map and Quantization on Sphere
• Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere
• Inequivalent Quantizations of Gauge Theories