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Advances in Applied Clifford Algebras

, Volume 22, Issue 4, pp 1129–1149 | Cite as

Majorana–Oppenheimer Approach to Maxwell Electrodynamics. Part I. Minkowski Space

  • V. M. Red’kov
  • N. G. Tokarevskaya
  • George J. Spix
Article

Abstract

The Riemann–Silberstein–Majorana–Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation SO(3,C) group is demonstrated explicitly. For vacuum, the matrix form includes four real 4 × 4 matrices α b . In the presence of a medium the matrix form requires two sets of 4 × 4 matrices, α b and β b , simple and symmetrical realization of which is given. Minkowski constitutive relations in the case of arbitrary linear media are given in a short algebraic form based on the use of complex 3-vector fields. The matrix formulation in the Esposito’s form based on the use of two electromagnetic 4-vector is studied and discussed.

Keywords

Minkowski space Maxwell electrodynamics matrix formalism media complex rotation group 

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© Springer Basel AG 2012

Authors and Affiliations

  • V. M. Red’kov
    • 1
  • N. G. Tokarevskaya
    • 2
  • George J. Spix
    • 3
  1. 1.B.I. Stepanov Institute of PhysicsNational Academy of Sciences of BelarusMinskBelarus
  2. 2.Belorussian State Economical UniversityMinskBelarus
  3. 3.BSEE Illinois Institute of TechnologyUrbanaUSA

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