The role of the Pauli-Luba ski vector for the Dirac, Weyl, Proca, Maxwell and Fierz-Pauli equations

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-Luba ski vector and the Casimir operators of the Poincaré...

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Bibliographic Details
Published in:Physica scripta 2016-02, Vol.91 (3)
Main Authors: Kryuchkov, Sergey I, Lanfear, Nathan A, Suslov, Sergei K
Format: Article
Language:English
Subjects:
Dirac equation
Maxwell equations
Pauli-Luba ski vector
Poincare group
Proca equation
Weyl equation
Online Access:Get full text
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Summary: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-Luba ski vector and the Casimir operators of the Poincaré 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.
ISSN:0031-8949
1402-4896
DOI:10.1088/0031-8949/91/3/035301