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

Sergey I. Kryuchkov, Nathan A. Lanfear, Sergei Suslov

Research output: Contribution to journalArticle

1 Scopus citations

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-Lubański vector and the Casimir operators of the Poincarégroup. 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.

Original languageEnglish (US)
Article number035301
JournalPhysica Scripta
Volume91
Issue number3
DOIs
StatePublished - Feb 16 2016

Keywords

  • Dirac equation
  • Maxwell equations
  • Pauli-Lubanski vector
  • Poincare group
  • Proca equation
  • Weyl equation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics

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