Yang-Mills gauge fields conserving the symmetry algebra of the Dirac equation in a homogeneous space

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Abstract

We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are found by comparison of the Dirac equation with an invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The eigenfunctions and the corresponding eigenvalues for the Dirac equation are obtained in the space R<sup>2</sup> × S<sup>2</sup> by a noncommutative integration method.

Original languageEnglish
Article number012004
JournalJournal of Physics: Conference Series
Volume563
Issue number1
DOIs
Publication statusPublished - 26 Nov 2014

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Dirac equation
algebra
symmetry
Yang-Mills fields
differential operators
eigenvectors
eigenvalues

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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abstract = "We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are found by comparison of the Dirac equation with an invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The eigenfunctions and the corresponding eigenvalues for the Dirac equation are obtained in the space R2 × S2 by a noncommutative integration method.",
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AB - We consider the Dirac equation with an external Yang-Mills gauge field in a homogeneous space with an invariant metric. The Yang-Mills fields for which the motion group of the space serves as the symmetry group for the Dirac equation are found by comparison of the Dirac equation with an invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The eigenfunctions and the corresponding eigenvalues for the Dirac equation are obtained in the space R2 × S2 by a noncommutative integration method.

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