### 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 language | English (US) |
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Article number | 035301 |

Journal | Physica Scripta |

Volume | 91 |

Issue number | 3 |

DOIs | |

State | Published - 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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## Cite this

Kryuchkov, S. I., Lanfear, N. A., & Suslov, S. (2016). The role of the Pauli-Lubański vector for the Dirac, Weyl, Proca, Maxwell and Fierz-Pauli equations.

*Physica Scripta*,*91*(3), [035301]. https://doi.org/10.1088/0031-8949/91/3/035301