Higher spin quaternion waves in the Klein-Gordon theory

TL;DR

This paper explores a modified Klein-Gordon equation incorporating quaternion-like plane waves to describe higher spin particles, connecting to historical theories by Majorana, Gelfand, and Yaglom, and addressing electromagnetic interactions.

Contribution

It introduces a quaternion-based generalization of the Klein-Gordon equation that accounts for arbitrary spin states, extending previous theoretical frameworks.

Findings

Derived Mott scattering amplitude with a factor discrepancy.

Revealed the importance of polarization states in the modified equation.

Connected the mass-spin relation to earlier infinite spin theories.

Abstract

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories.