Hopf Map and Quantization on Sphere

Abstract

Quantization of a system constrained to move on a sphere is considered by taking a square root of the ``on sphere condition''. We arrive at the fibre bundle structure of the Hopf map in the cases of $S^2$and $S^4$. This leads to more geometrical understanding of monopole and instanton gauge structures that emerge in the course of quantization.

9 pages, LaTeX2e, uses amsmath.sty

References in corpus (1)

• Quantum Mechanics on S^n and Meron Solution

Cited by in corpus (2)

• Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere
• Riemannian Gauge Theory and Charge Quantization