Dirac-KÄhler Equation

Details Dirac-KÄhler Equation Dirac-KÄhler Equation

2001-10-27

arxiv.org/abs/hep-th/0110251v3

Int. J. Theor. Phys. 41 (2002) 653-687

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, LaTeX. Corrections in Eqs. (29), (88), (99). Extended version of hep-th/0110060

Scientific paper

Tensor, matrix and quaternion formulations of Dirac-K\"ahler 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-K\"ahler 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-K\"ahler fields with tensor and spinor parameters is investigated. We show the possibility of constructing a gauge model of interacting Dirac-K\"ahler fields where the gauge group is the noncompact group under consideration.

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