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Clifford Algebras pp 431–450Cite as

Chiral Dirac Equations

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Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

Abstract

A chiral relativistic wave equation is proposed for neutrinos. This wave equation allows a mass term. We study this equation in the Clifford algebra of space, and in the frame of the Clifford spacetime algebra, second-order equation, plane waves, Lagrangian formalism, conservative current. Next we extend the wave equation to the complete spacetime algebra and we obtain a chiral wave equation with a mass term and a charge term. We study the relativistic invariance, the Lagrangian formalism, the second-order equation, we solve the equation in the case of the hydrogen atom. We obtain the right number of energy levels and the right energy levels. We study the enlargement of the gauge invariance, with a real matrix formalism. The electric gauge group may be extended to SO(8), a subgroup of SO(16).

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Author information

Authors and Affiliations

  1. La Lande, 44522, Pouillé-les-coteaux, France

    Claude Daviau

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  1. Claude Daviau
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, 5054, TN 38505, Cookeville, USA

    Rafał Abłamowicz

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© 2004 Birkhäuser Boston

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Daviau, C. (2004). Chiral Dirac Equations. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_28

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  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_28

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

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