2012/11/18 by E. Ovsiyuk, Ovsiyuk, E., О. В. Веко +3
Physics and Astronomy · #35 #Atomic and Subatomic Physics Research #FOS: Physical sciences #G.1 #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1211.4236
openalex publication_date 2012/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Properties of tensors equivalent to the direct product of two different 4-spinors are investigated. It is shown that the tensors obey additional 8 nonlinear restrictions, those are presented in Lorentz covariant form. In the context of the Dirac-Kähler theory, such a property can be interpreted as follows: if one wishes to consider the Dirac-Kähler field as consisting of two 4-spinor fields, one must impose additional restrictions on tensors of the Dirac-Kähler field, which leads to a non-linear wave equation for a complex boson field (composed on the base of two 4-spinor fields). Instead, the use of four bi-spinor fields gives possibility to construct the Dirac-Kähler tensor set of 16 independent components. However, the formulas relating the Dirac-Kähler boson to four fermion fields are completely different from those previously used in the literature. In explicit form, restrictions on four 4-spinor corresponding to separation of different simplest bosons with spin 0 or 1 and various intrinsic parities, are constructed.