# Spin Angular Momentum of Proton Spin Puzzle in Complex Octonion Spaces

## TL;DR

This paper uses complex octonion mathematics to analyze the proton spin puzzle, revealing additional components of angular momentum and proposing new precessional motions that contribute to understanding proton spin structure.

## Contribution

It introduces a novel decomposition of proton angular momentum into six components using complex octonion space, offering new insights into the proton spin puzzle.

## Key findings

- External electromagnetic strength induces new precessional motion.
- Proton angular momentum decomposes into more components than previously recognized.
- Orbital angular momentum and magnetic dipole moment are independent and should be measured separately.

## Abstract

The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially the proton spin, decomposition, quarks and gluons, and polarization and so forth. J. C. Maxwell was the first to use the quaternions to study the electromagnetic fields. Subsequently the complex octonions are utilized to depict the electromagnetic field, gravitational field, and quantum mechanics and so forth. In the complex octonion space, the precessional equilibrium equation infers the angular velocity of precession. The external electromagnetic strength may induce a new precessional motion, generating a new term of angular momentum, even if the orbital angular momentum is zero. This new term of angular momentum can be regarded as the spin angular momentum, and its angular velocity of precession is different from the angular velocity of revolution. The study reveals that the angular momentum of the proton must be separated into more components than ever before. In the proton spin puzzle, the orbital angular momentum and magnetic dipole moment are independent of each other, and they should be measured and calculated respectively.