Abstract
Abstract
We derive a formalism to express the spin algebra
s
u
(
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 (2003 J. Phys. A: Math. Gen.
36 L503) who in turn clarified on an inconsistency within a similar formalism in the works of Batista and Ortiz (2001 Phys. Rev. Lett.
86 1082). 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.
Funder
Deutsche Forschungsgemeinschaft
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics