  Analyzing the representations of the Lorentz group, we give a systematic
count and construction of all the possible Lagrangians describing an
antisymmetric rank two tensor field. The count yields two scalars: the gauge
invariant Kalb-Ramond model, equivalent to the sigma model and familiar from
super gravity and string theory, and the conformally invariant Avdeev-Chizhov
model, which describes self-dual tensors. The count also includes a third
invariant, a pseudoscalar, which is an antisymmetrized form of the
Avdeev-Chizhov Lagrangian, first noticed in the $SU(2/1)$ superalgebraic model
of the weak interactions. This model is also conformally invariant, and
naturally implements the Landau $CP$ symmetry. Then, by extending the
Duffin-Kemmer-Petiau 10 component formalism, we recover the model Lagrangians
as first order systems. To complete the analysis we classify all local Lorentz
invariant potentials (mass terms and quartic couplings) for charged
antisymmetric tensor fields coupled to a Yang-Mills field.
