Quaternion Electromagnetism and the Relation with 2-Spinor Formalism

Abstract

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary 'i' should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotation

arXiv commentVersion published in journal Universe (2019)

References in corpus (8)

• Octonic Electrodynamics
• Quaternions and Special Relativity
• Octonion Quantum Chromodynamics
• Quaternion Gravi-Electromagnetism
• Field Equations in the Complex Quaternion Spaces
• Quaternion algebra on 4D superfluid quantum space-time. Gravitomagnetism
• Hydrodynamics of Superfluid Quantum Space: particle of spin-1/2 in a magnetic field
• The Cayley-Dickson Construction in ACL2

Cited by in corpus (4)

• Quaternionic electrodynamics
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• QED based on eight-dimensional spinorial wave equation of the electromagnetic field and the emergence of quantum gravity
• Curvature Spinors in Locally Inertial Frame and the Relations with Sedenion