A Mapping between the Spin and Fermion Algebra

Abstract

We derive a formalism to express the spin algebra su(2) in a spin s representation in terms of the algebra of L fermionic operators that obey the Canonical Anti-commutation Relations. We also give the reverse direction of expressing the fermionic operators as polynomials in the spin operators of a single spin. We extend here to further spin values the previous investigations by Dobrov [J.Phys.A: Math. Gen 36 L503, (2003)] who in turn clarified on an inconsistency within a similar formalism in the works of Batista and Ortiz [Phys. Rev. Lett. 86, 1082 (2001)]. We then consider a system of L fermion flavors and apply our mapping in order to express it in terms of the spin algebra. Furthermore we investigate a possibility to simplify certain Hamiltonian operators by means of the mapping.