Some Consequences from the Dirac – Kähler Theory: On Intrinsic Spinor Sub-Structure of the Different Boson Wave

Properties of tensors equivalent to the direct product of two different 4-spinors are investigated. It is shown that tensors obey eight additional nonlinear restrictions, which are presented in the Lorentz covariant form. In the context of the Dirac–Kähler theory, such a property can be interpreted as follows: if one considers a Dirac–Kähler field as consisting of two 4-spinor fields, one should impose additional restrictions on tensors of the Dirac–Kähler field, that leads to a non-linear wave equation for a complex boson field (composed 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 literature. In an explicit form, the restrictions on four 4-spinors corresponding to separation of different simplest bosons with spin 0 or 1 and various intrinsic parities, are constructed