  We complete the first stage of constructing a theory of fields not
investigated before; these fields transform according to Lorentz group
representations decomposable into an infinite direct sum of finite-dimensional
irreducible representations. We consider only those theories that initially
have a double symmetry: relativistic invariance and the invariance under the
transformations of a secondary symmetry generated by the polar or the axial
four-vector representation of the orthochronous Lorentz group. The high
symmetry of the theory results in an infinite degeneracy of the particle mass
spectrum with respect to spin. To eliminate this degeneracy, we postulate a
spontaneous secondary-symmetry breaking and then solve the problems on the
existence and the structure of nontrivial interaction Lagrangians.
