Varieties of Dirac equation and flavors of leptons and quarks

Ruo Peng Wang

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arXiv · hep-ph/0107184

Varieties of Dirac equation and flavors of leptons and quarks

Ruo Peng Wang

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Abstract

I show that there exist twelve independent Dirac equations for spin 1/2 fermions. The Dirac fields that satisfy these equations can be grouped into six pairs according to the way they transform under continuous space-time transformations. These six pairs of Dirac equations correspond to the three quark generations and the three lepton generations. The charged V-A currents can be formed only from fields of the same pair. This property of the Dirac fields implies that a quark or lepton may be transformed only into its partner of the same generation via the charged-current weak interaction. According to the properties of the charged-current weak interaction, I conclude that different elementary fermion fields must satisfy different Dirac equations, and there may not be more than twelve flavors of elementary fermions that are already known.

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Ruo Peng Wang. 2001-07-29. Varieties of Dirac equation and flavors of leptons and quarks. https://arxiv.org/abs/hep-ph/0107184

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