The conclusion of the Dirac matrices in the real, complex and quaternionic representations

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.

Keywords

Dirac matrices / covariant associative algebra / Clifford algebra / structural constants / structural matrixes

References

[1] Кецарис А.А. Алгебраические основы физики. Пространство-время и действие как универсальные алгебры, М., Издательство УРСС, 2004, 280с.

[2] Hestenes D., Weingartshofer A. The electron, new theory and experiment, Kluwer Academic Publishers, Dordrecht, 1991.

[3] Hestenes D., Sobczyk G. Clifford algebra in geometric calculus, Riedel Publishing Company, Dordrecht, 1984.

RIGHTS & PERMISSIONS

Ketsaris A.A.