2001/10/31 by S. I. Kruglov
Physics and Astronomy · #hep-th
published as Int. J. Theor. Phys. 41 (2002) 653-687 · 42 pages, LaTeX. Corrections in Eqs. (29), (88), (99). Extended version of hep-th/0110060
arxiv created 2003/04/07 · arxiv updated 2009/11/30
Tensor, matrix and quaternion formulations of Dirac-Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found. A method of computing the traces of 16-dimensional Petiau-Duffin-Kemmer matrix product is considered. We show that the symmetry group of the Dirac-Kähler tensor fields for charged particles is SO(4,2). The conservation currents corresponding this symmetry are constructed. We analyze transformations of the Lorentz group and quaternion fields. Supersymmetry of the Dirac-Kähler fields with tensor and spinor parameters is investigated. We show the possibility of constructing a gauge model of interacting Dirac-Kähler fields where the gauge group is the noncompact group under consideration.