2001/07/17 by Ruo Peng Wang, Wang, Ruo Peng
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/0107184
5 pages, RevTeX
arxiv created 2001/07/29 · arxiv updated 2009/11/30
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.