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arXiv · 1510.05164

The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, Maxwell, and Fierz-Pauli Equations

Sergey I. Kryuchkov·Nathan A. Lanfear·Sergei K. Suslov
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Abstract

We analyze basic relativistic wave equations for the classical fields, such as Dirac's equation, Weyl's two-component equation for massless neutrinos, and the Proca, Maxwell, and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir operators of the Poincare group. In general, in this group-theoretical approach, the above wave equations arise in certain overdetermined forms, which can be reduced to the conventional ones by a Gaussian elimination. A connection between the spin of a particle/field and consistency of the corresponding overdetermined system is emphasized in the massless case.

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Sergey I. Kryuchkov, Nathan A. Lanfear, Sergei K. Suslov. 2016-01-22. The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, Maxwell, and Fierz-Pauli Equations. https://doi.org/10.1088/0031-8949%2F91%2F3%2F035301

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