Unitary representations of the Wigner group $ISL(2,\mathbb C)$ and a two-spinor description of massive particles with an arbitrary spin

Based on Wigner unitary representations for the covering group $ISL(2,\mathbb C)$ of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with an arbitrary spin that satisfy the Dirac–Pauli–Fierz equations. In the framework of a two-spinor formalism, we construct spin-polarization vectors and obtain conditions that fix the corresponding density matrices (the Berends–Fronsdal projection operators) determining the numerators in the propagators of the fields of such particles. Using these conditions, we find explicit expressions for the particle density matrices with integer (Berends–Fronsdal projection operators) and half-integer spin. We obtain a generalization of the Berens–Fronsdal projection operators to the case of an arbitrary number $D$ of space–time dimensions.