Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian space-time
Bogush, A. ; Red'kov, V. ; Tokarevskaya, N. ; Spix, G.
arXiv, 0905.0261 / Harvested from arXiv
Text on arXiv
The Riemann -- Silberstein -- Majorana -- Oppengeimer 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 group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \times 4$ matrices $\alpha^{b}$. In presence of media matrix form requires two sets of $4 \times 4$ matrices, $\alpha^{b}$ and $\beta^{b}$ -- simple and symmetrical realization of which is given. Relation of $\alpha^{b}$ and $\beta^{b}$ to the Dirac matrices in spinor basis is found. Minkowski constitutive relations in case of any linear media are given in a short algebraic form based on the use of complex 3-vector fields and complex orthogonal rotations from SO(3.C) group. The matrix complex formulation in the Esposito's form, based on the use of two electromagnetic 4-vector, is studied and discussed. Extension of the 3-vector complex matrix formalism to arbitrary Riemannian space-time in accordance with tetrad method by Tetrode-Weyl-Fock-Ivanenko is performed.
Publié le : 2009-05-03
Classification:  Mathematical Physics,  High Energy Physics - Theory 
@article{0905.0261,
     author = {Bogush, A. and Red'kov, V. and Tokarevskaya, N. and Spix, G.},
     title = {Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian
  space-time},
     journal = {arXiv},
     volume = {2009},
     number = {0},
     year = {2009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0905.0261}
}

Bogush, A.; Red'kov, V.; Tokarevskaya, N.; Spix, G. Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian
  space-time. arXiv, Tome 2009 (2009) no. 0, . http://gdmltest.u-ga.fr/item/0905.0261/