Generalization of the Bargmann-Wigner approach to constructing relativistic fields

We review the method for constructing local relativistic fields corresponding to the Bargmann-Wigner wave functions that describe the unitary irreducible representations of the $4D$ Poincaré group. The method is based on the use of the generalized Wigner operator connecting the wave functions of induced representations and local relativistic fields. Applications of this operator for constructing massive local relativistic fields as well as massless helicity local fields and massless local infinite spin fields are considered.