TITLE:
A Real Version of the Dirac Equation and Its Coupling to the Electromagnetic Field
AUTHORS:
Eckart Marsch
KEYWORDS:
Dirac Equation, Coupling to Electromagnetic Field, Real Field Equation
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.1,
January
14,
2015
ABSTRACT: A real
version of the Dirac equation is derived and its coupling to the
electromagnetic field considered. First the four-component real Majorana equation
is briefly discussed. Then the complex Dirac equation including an
electromagnetic field will be written as an eight-component real spinor equation
by separating it into its real and imaginary parts. Through this decomposition,
what becomes obvious is the way in which the electromagnetic field couples to
charged fermions (electron and positron) when being described by real spinor
fields. Thus, contrary to common expectation, charged fermions can also be
described by a real Dirac equation if they are considered as a doublet related to
the SO(2) symmetry group, which enables a matrix coupling to the
electromagnetic field and corresponds to the usual U(1) gauge symmetry of the
standard Dirac equation.