A Mapping between the Spin and Fermion Algebra
Abstract
We derive a formalism to express the spin algebra in a spin representation in terms of the algebra of 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 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.
Cite
@article{arxiv.2101.10119,
title = {A Mapping between the Spin and Fermion Algebra},
author = {Felix Meier and Daniel Waltner and Petr Braun and Thomas Guhr},
journal= {arXiv preprint arXiv:2101.10119},
year = {2021}
}