What particles are described by the Weinberg theory?

The main goal of the paper is to study the origins of a contradiction between the Weinberg theorem B - A = lambda and the 'longitudity' of an antisymmetric tensor field (and of a Weinberg field which is equivalent to it), transformed on the (1, 0) + (0, 1) Lorentz group representation. On the basis of analysis of dynamical invariants in the Fock space situation has been partly clarified. The interest in the 2(2j + 1) component model [1, 2, 3, 4] and in the antisymmetric tensor fields [5, 6] has grown in the last years. Antisymmetric tensor fields are of importance for physical applications [7]. Moreover, they are an object of continuous and renewed interests due to their connection with topological field theories [8].