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A Real Version of the Dirac Equation and Its Coupling to the Electromagnetic Field

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DOI: 10.4236/jmp.2015.61001    2,698 Downloads   3,371 Views  
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Eckart Marsch*

Affiliation(s)

Institute for Experimental and Applied Physics, Christian Albrechts University at Kiel, Kiel, Germany.

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.

KEYWORDS

Dirac Equation, Coupling to Electromagnetic Field, Real Field Equation

Cite this paper

Marsch, E. (2015) A Real Version of the Dirac Equation and Its Coupling to the Electromagnetic Field. Journal of Modern Physics, 6, 1-11. doi: 10.4236/jmp.2015.61001.

Conflicts of Interest

The authors declare no conflicts of interest.

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