2011/09/11 by Red'kov, V. M.
#35 #FOS: Physical sciences #G.1 #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1109.2310
A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then spinor equations for fermions. In that context, a very interesting problem is of extension a wave equation for Dirac--Kähler field (Ivanenko--Landau field was historically first term, also the term a vector field of general type was used). The article relates a generally covariant tensor formalism to a spinor one when these both are applied to description of the Dirac-Kähler field in a Rimannian space-time. Both methods are taken to be equivalent and the tensor equations are derived from spinor ones. It is shown that, for characterization of Dirac-Kähler's tensor components, two alternative approaches are suitable: these are whether a tetrad-based pseudo tensor classification or a generally coordinate pseudo tensor one. By imposing definite restrictions on the the Dirac-Kähler function, we have produced the general covariant form of wave equations for scalar, pseudoscalar, vector, and pseudovector particles.