Relativistic Quaternionic Wave Equation II

TL;DR

This paper advances the quaternionic wave equation theory by deriving new Lagrangians, exploring multi-particle tensor products, and clarifying foundational principles like linearity and superposition.

Contribution

It introduces new Lagrangians for the quaternionic wave equation and investigates multi-particle systems using tensor products of Hilbert spaces.

Findings

Derived a Lagrangian for the momentum-space free equation

Found a nonlocal-in-time Lagrangian for the complete equation

Clarified the principles of linearity and superposition in quaternionic quantum mechanics

Abstract

Further results are reported for the one-component quaternionic wave equation recently introduced. A Lagrangian is found for the momentum-space version of the free equation; and another, nonlocal in time, is found for the complete equation. Further study of multi-particle systems has us looking into the mathematics of tensor products of Hilbert spaces. The principles of linearity and superposition are also clarified to good effect in advancing the quaternionic theory.