Higher spin quaternion waves in the Klein-Gordon theory

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.

References in corpus (6)

• Considerations on the hyperbolic complex Klein-Gordon equation
• Revisiting Quaternionic Dual Electrodynamics
• Generalized Gravi-Electromagnetism
• CPT groups of higher spin fields
• Erlangen Programme at Large 3.1: Hypercomplex Representations of the Heisenberg Group and Mechanics
• Electromagnetic Klein-Gordon and Dirac equations in scale relativity

Cited by in corpus (5)

• Quaternionic Klein-Gordon equation
• A possibility of Klein Paradox in quaternionic (3+1) frame
• Conformal relativity with hypercomplex variables
• Klein-Gordon equation within the real Hilbert space formalism
• Lie sphere geometry in nuclear scattering processes