Open Access Fonds
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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Open Access Fonds Open Access Fonds
2021
Eckart Marsch,
Yasuhito Narita
doi:10.3390/sym13030475
Abstract: In this paper, we study possible mathematical connections of the Clifford algebra with the su(N)-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal SU(N) gauge-symmetry for a massive spin one-half fermion described by the Dirac equation. The related matrix algebra is worked out in particular for the SU(2) symmetry and outlined as well for the color gauge group SU(3). Possible perspectives of this approach to unification of symmetries are briefly discussed. The calculations make extensive use of tensor multiplication of the matrices involved, whereby our focus is on revisiting the Coleman–Mandula theorem. This permits us to construct unified symmetries between Lorentz invariance and gauge symmetry in a direct product sense. Keywords: extended Dirac equation; isospin; Clifford algebra; SU(N) symmetry Published Online: 2021/09/15 09:13:58 Object Identifier: 0xc1aa5576 0x003ccebe Rights: .
Der Open Access (OA) Fonds der ÖAW fördert, von der Bibliothek der ÖAW administriert, Open Access Publikationen von ÖAW-Angehörigen. Beim OA Fonds können Förderungen für Article Processing Costs (APCs) in Zeitschriften und für Publikation von Monographien, bzw. Beiträgen in Sammelwerken beantragt werden. |
Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |