Induced Gauge Structure of Quantum Mechanics on $S^D$

TL;DR

This paper explores the gauge structures induced in quantum mechanics on spheres, explicitly constructing generators and revealing how trivial gauge configurations can have nontrivial physical effects, with connections to monopole theories.

Contribution

It provides explicit constructions of generators satisfying the Ohnuki-Kitakado algebra and develops a covariant method to analyze induced gauge potentials on $S^D$.

Findings

Existence of trivial gauge configurations with nontrivial effects in higher dimensions

Explicit form of generators satisfying the O-K algebra

Relation to monopole configurations like the 't Hooft-Polyakov monopole

Abstract

The Ohnuki-Kitakado (O-K) scheme of quantum mechanics on $S^D$ embedded in $R^{D+1}$ is investigated. Generators satisfying the O-K algebra are written down explicitly in term of the induced gauge potential. A direct method is developed to obtain the generators in covariant form. It is seen that there exists an induced gauge configuration which is trivial on $S^D$ but might cause a nontrivial physical effect in $R^{D+1}$. The relation of the O-K scheme to extended objects such as the 't Hooft-Polyakov monopole is discussed.