Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions

Symmetry

Avraham Nofech¹ 

[1] Department of Mathematics and Statistics, MacEwan University, Edmonton, AB T5J 4S2, Canada;

关键词: Dirac Equation;    biquaternion;    Majorana;    mass;    Pauli algebra;    outer automorphism;   

DOI  :  10.3390/sym12071144

来源: DOAJ

【 摘 要 】

A biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image under an outer automorphism of the Pauli algebra. The charge conjugation operator takes a particulary simple form in this formulation and switches the sign of the mass coefficient, so that for a solution invariant under charge conjugation the mass has to equal zero. The multiple of the charge conjugation operator by the imaginary unit turns out to be a complex Lorentz transformation. It commutes with the outer automorphism, while the charge conjugation operator itself anticommutes with it, providing a second more algebraic proof of the main theorem. Considering the Majorana equation, it is shown that non-zero mass of its solution is imaginary.

【 授权许可】

Unknown