On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons
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...
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doaj-255c08888dab49da9c427e749b4afd812020-11-25T00:47:20ZengMDPI AGSymmetry2073-89942015-04-017245046310.3390/sym7020450sym7020450On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive LeptonsEckart Marsch0Institute for Experimental and Applied Physics, Christian Albrechts University at Kiel, Leibnizstraße 11, 24118 Kiel, GermanyWe 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.http://www.mdpi.com/2073-8994/7/2/450charge conjugationMajorana fieldschiral symmetry |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Eckart Marsch |
spellingShingle |
Eckart Marsch On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons Symmetry charge conjugation Majorana fields chiral symmetry |
author_facet |
Eckart Marsch |
author_sort |
Eckart Marsch |
title |
On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons |
title_short |
On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons |
title_full |
On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons |
title_fullStr |
On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons |
title_full_unstemmed |
On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons |
title_sort |
on charge conjugation, chirality and helicity of the dirac and majorana equation for massive leptons |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2015-04-01 |
description |
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. |
topic |
charge conjugation Majorana fields chiral symmetry |
url |
http://www.mdpi.com/2073-8994/7/2/450 |
work_keys_str_mv |
AT eckartmarsch onchargeconjugationchiralityandhelicityofthediracandmajoranaequationformassiveleptons |
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