Something about spin-fermion connection

TL;DR

This paper derives Jordan-Wigner-type transformations linking spin-3/2 operators to fermions, establishes conditions for fermionization of spins, and corrects previous generalization attempts, advancing theoretical understanding of spin-fermion connections.

Contribution

It introduces new transformations for spin-3/2 systems, provides a general fermionizability condition, and proves a theorem relating half-integer spins to fermions, correcting prior work.

Findings

Derived Jordan-Wigner-type transformations for spin-3/2.

Established a general condition for spin fermionization.

Identified errors in previous spin generalization attempts.

Abstract

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.