Octonionic Dirac Equation

Abstract

In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a translation is also given for $4\times 4$ complex matrices). We develop an octonionic relativistic free wave equation, linear in the derivatives. Even if the wave functions are only one-component we show that four independent solutions, corresponding to those of the Dirac equation, exist.

To appear in Prog. Theor. Phys. (vol 96)

References in corpus (3)

• Octonionic Quantum Mechanics and Complex Geometry
• One Component Dirac Equation
• Octonionic Representations of GL(8,R) and GL(4,C)

Cited by in corpus (19)

• Right eigenvalue equation in quaternionic quantum mechanics
• Octonionic Electrodynamics
• Quaternionic potentials in non-relativistic quantum mechanics
• Octonionic Quantum Mechanics and Complex Geometry
• Analytic Plane Wave Solutions for the Quaternionic Potential Step
• Octonic relativistic quantum mechanics
• Octonionic Representations of GL(8,R) and GL(4,C)
• Superconducting currents and charge gradients in the octonion spaces
• Sedeonic relativistic quantum mechanics
• The octonionic eigenvalue problem
• Precessional angular velocity and field strength in the complex octonion space
• Torques and angular momenta of fluid elements in the octonion spaces
• Color Confinement and Spatial Dimensions in the Complex-sedenion Space
• Some spin textures relevant to magnetic moments in the octonion spaces
• Nonassociative quantum theory, emergent probability, and coquasigroup symmetry
• Spin Angular Momentum of Proton Spin Puzzle in Complex Octonion Spaces
• Unified Octonionic Representation of the 10-13 Dimensional Clifford Algebra
• Octonions and Super Lie algebra
• An analysis of Rick Lockyer's "octonion variance sieve"