Abstract
We revisit the charge-conjugation operation for the Dirac equation in its chiral representation. A new decomposition of the Dirac spinor field is suggested and achieved by means of projection operators based on charge conjugation, which is discussed here in a non-standard way. Thus, two separate two-component Majorana-type field equations for the eigenfields of the charge-conjugation operator are obtained. The corresponding free fields are entirely separated without a gauge field, but remain mixed and coupled together through an electromagnetic field term. For fermions that are charged and, thus, subjected to the gauge field of electrodynamics, these two Majorana fields can be reassembled into a doublet, which is equivalent to a standard four-component Dirac spinor field. In this way, the Dirac equation is retained in a new guise, which is fully equivalent to that equation in its chiral form.
Highlights
According to the canonical standard model of elementary particle physics, leptons and quarks come in three flavors, are massless and, obey chiral symmetry, but they acquire mass through theHiggs [1,2] mechanism
Symmetry 2015, 7 oscillations [10] had been found in the past few decades, massive neutrinos have been discussed, and another very massive neutrino species has been considered in four-neutrino models [11], for example to explain the masses of the light neutrinos by the see-saw mechanism [10]
The purpose of the present paper is to show that the Dirac equation for a massive and charged fermion can be rewritten in terms of two two-component Majorana-like equations, which respectively govern two independent Pauli-spinor fields
Summary
According to the canonical standard model of elementary particle physics, leptons and quarks come in three flavors, are massless and, obey chiral symmetry, but they acquire mass through the. The Dirac equation [4] is fundamental in all of this and well understood; the nature of the neutrinos involved remains less clear Are they Dirac fermions or massive Majorana [5,6] particles? The purpose of the present paper is to show that the Dirac equation for a massive and charged fermion can be rewritten in terms of two two-component Majorana-like equations, which respectively govern two independent Pauli-spinor fields. The related field equations are developed on the basis of the chiral Dirac equation Their derivation employs projection operator techniques related to the charge conjugation operator, which is considered here in a new way following the recent work by Marsch [16,17].
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