A comparative study of quaternionic rotational Dirac equation and its interpretation

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.

arXiv comment23 pages, 2 tables "Accepted in IJGMMP"

References in corpus (14)

• Generalized Octonion Electrodynamics
• Octonic Electrodynamics
• Quaternions and Special Relativity
• Octonion Quantum Chromodynamics
• Quaternion Gravi-Electromagnetism
• The Quaternionic Dirac Lagrangian
• The Quaternionic Quantum Mechanics
• A new development in quantum field equations of dyons
• A relativistic quantum theory of dyons wave propagation
• Quaternionic particle in a relativistic box
• Quaternionic approach to dual Magneto-hydrodynamics of dyonic cold plasma
• Some properties of dark matter field in the complex octonion space
• Delay Time in Quaternionic Quantum Mechanics
• Quaternion Dirac Equation and Supersymmetry

Cited by in corpus (10)

• Quaternionic elastic scattering
• Quaternionic electrodynamics
• Quaternionic Dirac free particle
• On the quaternion transformation and field equations in curved space-time
• Generalized quaternionic free rotational Dirac equation and spinor solutions in the electromagnetic field
• A possibility of Klein Paradox in quaternionic (3+1) frame
• Gauge fields and four interactions in the trigintaduonion spaces
• Z_2 Graded Lie Algebra of Quaternions and Superconformal Algebra in D=4 dimensions
• On the group theoretical approach to relativistic wave equations for arbitrary spin
• On the existence of quaternion-handedness for the spinor solutions of the Dirac and Majorana neutrinos