Generalization of the Majorana equation for real spinors

We show that the Dirac equation for real spinors can be naturally decomposed into a system of two first-order relativistic wave equations. The decomposition separates in a transparent way the real and imaginary parts of the Dirac equation by means of two algebraic differential operators, allowing to...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Pérez Teruel, Ginés R
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.04.2016
Subjects
Decomposition
Differential equations
Dirac equation
Mathematical analysis
Operators (mathematics)
Relativism
Relativistic effects
Wave equations
Online AccessGet full text

Cover

More Information
Summary:We show that the Dirac equation for real spinors can be naturally decomposed into a system of two first-order relativistic wave equations. The decomposition separates in a transparent way the real and imaginary parts of the Dirac equation by means of two algebraic differential operators, allowing to describe real spinors in any representation of the Dirac matrices maintaining the reality condition \(\tilde{\Psi}=\tilde{\Psi}^{*}\) unaltered. In addition, it is shown that the Majorana wave equation is a particular case of the relativistic system of equations deduced in this paper. We also briefly discuss how the formalism can be extended to deal with complex (charged) spinors.
ISSN:2331-8422