### 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 |

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### 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

*Physica Scripta*,

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

**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.

Research output: Contribution to journal › Article

*Physica Scripta*, vol. 91, no. 3, 035301. https://doi.org/10.1088/0031-8949/91/3/035301

}

TY - JOUR

T1 - The role of the Pauli-Lubański vector for the Dirac, Weyl, Proca, Maxwell and Fierz-Pauli equations

AU - Kryuchkov, Sergey I.

AU - Lanfear, Nathan A.

AU - Suslov, Sergei

PY - 2016/2/16

Y1 - 2016/2/16

N2 - 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.

AB - 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.

KW - Dirac equation

KW - Maxwell equations

KW - Pauli-Lubanski vector

KW - Poincare group

KW - Proca equation

KW - Weyl equation

UR - http://www.scopus.com/inward/record.url?scp=84960421816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960421816&partnerID=8YFLogxK

U2 - 10.1088/0031-8949/91/3/035301

DO - 10.1088/0031-8949/91/3/035301

M3 - Article

AN - SCOPUS:84960421816

VL - 91

JO - Physica Scripta

JF - Physica Scripta

SN - 0031-8949

IS - 3

M1 - 035301

ER -