Quaternionic Dirac free particle

Abstract

We solve the quaternionic Dirac equation ($\mathbbm H$DE) in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solution set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation ($\mathbbm C$DE). These free particle solutions were unknown in the previous solutions of anti-hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory ($\mathbbm H$QFT).

Accept by Int. J. Mod. Phys. A

References in corpus (6)

• Virial theorem and generalized momentum in quaternic quantum mechanics
• Quaternions, Lorentz Group and the Dirac Theory
• Quaternionic Klein-Gordon equation
• Quaternionic quantum harmonic oscillator
• Quaternion Dirac Equation and Supersymmetry
• Quaternionic elastic scattering

Cited by in corpus (2)

• Quaternionic scalar field in the real Hilbert space
• Quaternionic fermionic field