A mapping between the spin and fermion algebra. (3rd August 2021)

• Record Type: Journal Article
• Authors: Meier, Felix; Waltner, Daniel; Braun, Petr; Guhr, Thomas
• Is Part Of: Journal of physics. Volume 54:Number 34(2021)
• Publication Date: 2021-08-03
• Subjects: fermions -- spin algebra -- Jordan–Wigner transformation; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac13dc
• Languages: English
• ISSNs: 1751-8113

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.