A comparative study of quaternionic rotational Dirac equation and its interpretation

TL;DR

This paper develops a quaternionic rotational Dirac equation for spin-half particles, incorporating rotational energy and angular momentum, and explores its solutions and physical implications in quaternionic algebra.

Contribution

It introduces a generalized quaternionic Dirac equation with rotational components and derives solutions using quaternionic spinors, advancing the understanding of rotational effects in relativistic quantum mechanics.

Findings

Quaternionic Dirac equation includes rotational energy and angular momentum.

Solutions reveal dual energy and momentum components.

Quaternionic plane wave solutions describe rotational frequency and propagation.

Abstract

In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-half particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists the rotational energy and angular momentum of particle and anti-particle. Accordingly, we also discuss the four vector form of quaternionic relativistic mass, moment of inertia and rotational energy-momentum in Euclidean space-time. The quaternionic four angular momentum (i.e. the rotational analogy of four linear momentum) predicts the dual energy (rest mass energy and pure rotational energy) and dual momentum (linear like momentum and pure rotational momentum). Further, the solutions of quaternionic rotational Dirac energy-momentum are obtained by using one, two and four-component of quaternionic spinor. We also demonstrate the solutions of quaternionic plane wave equation which gives the rotational frequency and wave propagation vector of Dirac particles and anti-particles in terms of quaternionic form.