  The main goal of the paper is to study the origins of a contradiction between
the Weinberg theorem B-A=\lambda and the `longitudinality' of an antisymmetric
tensor field (and of a Weinberg field which is equivalent to it), transformed
on the (1,0)\oplus (0,1) Lorentz group representation. On the basis of analysis
of dynamical invariants in the Fock space situation has been partly clarified.
