BPST instanton and Spin from inequivalent quantizations

TL;DR

This paper introduces a new approach to quantization on coset spaces, linking inequivalent quantizations to physical phenomena like spin and BPST instantons, offering a fresh perspective on their origins.

Contribution

It proposes a simplified reformulation of inequivalent quantizations using Dirac's constrained systems approach, applied to the four-sphere, connecting mathematical quantization to physical entities.

Findings

Inequivalent quantizations induce relativistic spin.

They also give rise to a background BPST instanton.

The approach offers a natural account of these physical entities.

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 ${\rm G \rightarrow G/H}$ and employs a generalized form of Dirac's approach to the quantization of constrained systems. When applied to the four-sphere $S^4 \simeq {\rm Spin(5)/Spin(4)}$, the inequivalent quantizations induce relativistic spin and a background BPST instanton; thus they might provide a natural account of both of these physical entities.