  In the framework of the classical field theory a mapping between
antisymmetric tensor matter fields and Weinberg's $2(2j+1)$ component
"bispinor" fields is considered. It is shown that such a mapping exists and
equations which describe the $j=1$ antisymmetric tensor field coincide with the
Hammer-Tucker equations completely and with the Weinberg ones within a
subsidiary condition, the Klein-Gordon equation. A new Lagrangian for the
Weinberg theory is proposed. It is scalar, Hermitian and contains only the
first-order time derivatives of the fields. The remarkable feature of this
Lagrangian is the presence of dual field functions, considered as parts of a
parity doublet. I study then origins of appearance of the dual solutions in the
Weinberg equations on the basis of spinorial analysis and point out the topics
which have to be explained in the framework of a secondary quantization scheme.
