Quantization of Massless Fields with Continuous Spin

Quantization is carried out of massless fields with continuous spin that correspond to particular cases of irreducible unitary representations of the Poincaré group. On the basis of the covariant field equations, obtained by Wigner, Lorentz- and gauge-covariant commutation relations and Hamiltonian densities are explicitly obtained. Our main conclusions are as follows. For the case of a single- (double-) valued representation the covariant local Hamiltonian density result only from Fermi- (Bose-) quantization, whereas the causal commutation relations result only from Bose- (Fermi-) quantization. A consistent quantum field theory is therefore impossible for any of these cases.