The Role of the Pauli-Lubanski 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-Lubanski vector and the Casimir operators of the Poincar...

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Hauptverfasser: Kryuchkov, Sergey I, Lanfear, Nathan A, Suslov, Sergei K
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description 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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subjects Gaussian elimination
Mathematical analysis
Mathematics - Mathematical Physics
Neutrinos
Particle spin
Physics - Mathematical Physics
Physics - Quantum Physics
Wave equations
title The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, Maxwell, and Fierz-Pauli Equations
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