Some Consequences from the Dirac-Kahler Theory: on Intrinsic Spinor Sub-structure of the Different Boson Wave Functions

TL;DR

This paper explores the tensor properties of Dirac-Kähler fields, revealing nonlinear restrictions and proposing a new framework involving four bi-spinor fields to better understand boson wave functions and their intrinsic spinor sub-structure.

Contribution

It introduces nonlinear restrictions on tensors from Dirac-Kähler theory and proposes a novel approach using four bi-spinor fields to describe boson wave functions.

Findings

Additional nonlinear restrictions on tensor structures are derived.

A new formulation relating Dirac-Kähler fields to four fermion fields is proposed.

Explicit restrictions for separating different bosons are constructed.

Abstract

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-K\"{a}hler theory, such a property can be interpreted as follows: if one wishes to consider the Dirac-K\"{a}hler field as consisting of two 4-spinor fields, one must impose additional restrictions on tensors of the Dirac-K\"{a}hler 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-K\"{a}hler tensor set of 16 independent components. However, the formulas relating the Dirac-K\"{a}hler 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.