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 Citation (Scopus)

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

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wave equations
Paul Adrien Maurice Dirac
Wave equation
Gaussian elimination
Overdetermined Systems
Dirac Equation
Dirac equation
Neutrinos
neutrinos
operators
Operator
Form

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

Cite this

The role of the Pauli-Lubański vector for the Dirac, Weyl, Proca, Maxwell and Fierz-Pauli equations. / Kryuchkov, Sergey I.; Lanfear, Nathan A.; Suslov, Sergei.

In: Physica Scripta, Vol. 91, No. 3, 035301, 16.02.2016.

Research output: Contribution to journalArticle

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