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Вывод матриц Дирака в действительном, комплексном и кватернионном представлениях

А. А. Кецарис

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Abstract

The article examines the relationship between the laws of the multiplication of vectors in the covariant Clifford algebra and Dirac matrices. The result is that spatial Dirac matrices are recorded in the form of a matrix structural permanent Clifford algebra over a geometric space. Spatio-temporal Dirac matrices represent the structural constants of the condensed Clifford algebra on the space-time. The structural constants are considered on the set of real numbers, complex numbers and quaternions.

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The article examines the relationship between the laws of the multiplication of vectors in the covariant Clifford algebra and Dirac matrices. The result is that spatial Dirac matrices are recorded in the form of a matrix structural permanent Clifford algebra over a geometric space. Spatio-temporal Dirac matrices represent the structural constants of the condensed Clifford algebra on the space-time. The structural constants are considered on the set of real numbers, complex numbers and quaternions.

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Available abstract

The article examines the relationship between the laws of the multiplication of vectors in the covariant Clifford algebra and Dirac matrices. The result is that spatial Dirac matrices are recorded in the form of a matrix structural permanent Clifford algebra over a geometric space. Spatio-temporal Dirac matrices represent the structural constants of the condensed Clifford algebra on the space-time. The structural constants are considered on the set of real numbers, complex numbers and quaternions.

Key concepts: Clifford algebra, Gamma matrices, Geometric algebra, Dirac algebra, Clifford analysis, Multivector, Classification of Clifford algebras, Quaternion

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Вывод матриц Дирака в действительном, комплексном и кватернионном представлениях — Research Paper | ScholarLens