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

doi:10.1088/0031-8949/91/3/035301

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 journal › Article › peer-review

5 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 language	English (US)
Article number	035301
Journal	Physica Scripta
Volume	91
Issue number	3
DOIs	https://doi.org/10.1088/0031-8949/91/3/035301
State	Published - Feb 16 2016

Keywords

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

ASJC Scopus subject areas

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

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10.1088/0031-8949/91/3/035301

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title = "The role of the Pauli-Luba{\'n}ski vector for the Dirac, Weyl, Proca, Maxwell and Fierz-Pauli equations",

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-Luba{\'n}ski vector and the Casimir operators of the Poincar{\'e}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.",

keywords = "Dirac equation, Maxwell equations, Pauli-Lubanski vector, Poincare group, Proca equation, Weyl equation",

author = "Kryuchkov, {Sergey I.} and Lanfear, {Nathan A.} and Sergei Suslov",

note = "Funding Information: This research was partially supported by NSF grants DMS # 1535833 and DMS # 1151618. We are indebted to Professor Dr Albert Boggess, Professor Dr Mark P Faifman, Professor Dr Gerald A Goldin, Professor Dr John Klauder, Professor Dr Margarita A Man''ko, Professor Dr Vladimir I Man''ko, Professor Dr Svetlana Roudenko and Professor Dr Igor N Toptygin for their valuable comments and encouragement. Comments from the referees, which have helped to improve the presentation, are much appreciated. Publisher Copyright: {\textcopyright} 2016 The Royal Swedish Academy of Sciences.",

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doi = "10.1088/0031-8949/91/3/035301",

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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

N1 - Funding Information: This research was partially supported by NSF grants DMS # 1535833 and DMS # 1151618. We are indebted to Professor Dr Albert Boggess, Professor Dr Mark P Faifman, Professor Dr Gerald A Goldin, Professor Dr John Klauder, Professor Dr Margarita A Man''ko, Professor Dr Vladimir I Man''ko, Professor Dr Svetlana Roudenko and Professor Dr Igor N Toptygin for their valuable comments and encouragement. Comments from the referees, which have helped to improve the presentation, are much appreciated. Publisher Copyright: © 2016 The Royal Swedish Academy of Sciences.

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

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

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VL - 91

JO - Physica Scripta

JF - Physica Scripta

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

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Keywords

ASJC Scopus subject areas

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