Something about spin-fermion connection

Jordan-Wigner-type transformations connecting the spin-3/2 operators and two kinds of fermions are derived. A general condition of fermionizability of spins is obtained and a theorem establishing connection between half integer spins and fermions is proved. The fallibility of a previous attempt to generalize the Jordan-Wigner transformation for all spins (C.D. Batista and G. Ortiz, Phys. Rev. Lett. 86, 1082 (2001)) is pointed out.