Dirac-Kähler Equation (Review)

Abstract

Tensor and matrix 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. It is shown that the symmetry group of the Dirac-Kähler tensor fields is SO(4,2). The conservation currents corresponding this symmetry are constructed. Supersymmetry of the Dirac-Kähler fields with tensor and spinor parameters is analyzed. We show the possibility of constructing a gauge model of interacting Dirac-Kähler fields where the gauge group is the noncompact group under consideration.

34 pages, LaTeX

References in corpus (2)

• Gluelump spectrum in the QCD string model
• Classifying Reported and "Missing" Resonances According to Their P and C Properties

Cited by in corpus (10)

• Dirac-Kähler particle in Riemann spherical space: boson interpretation
• Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators
• The Poincare lemma for codifferential, anticoexact forms, and applications to physics
• General form of the covariant field equations of arbitrary spin and the relativistic canonical quantum mechanics
• The Standard Model via Dirac-Kahler spinors
• Matter on granular space-time
• Relativistic Wave Equation for Fields with Two Mass and Spin States
• Minimal gauging of Dirac, Kahler, and Dirac-Kahler spinors
• Self-Dual Fields and Quaternion Analyticity
• Kalb-Ramond field and Dirac-Kahler equation