Proton spin: a topological invariant

TL;DR

This paper proposes a novel topological perspective on proton spin, suggesting it as a topological invariant represented by a de Rham 3-period, challenging traditional spin decomposition concepts.

Contribution

It introduces a topological invariant framework for proton spin using de Rham 3-periods and extends Finkelstein-Rubinstein theory to topological defects with nonabelian de Rham theorems.

Findings

Proton spin can vary continuously from 0 to ħ/2 in this model.

Spin is interpreted as a topological invariant, not decomposable into constituent parts.

Wilson lines and loop operators probe the topological properties related to spin.

Abstract

Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein-Rubinstein theory for Skyrmions/kinks to topological defects, and using nonabelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to $\frac{\hbar}{2}$, i. e. proton spin decomposition has no meaning in this approach.