A Mapping between the Spin and Fermion Algebra

• URL: http://arxiv.org/abs/2101.10119v2
• Date: Tue, 10 Aug 2021 11:54:28 GMT
• Title: A Mapping between the Spin and Fermion Algebra
• Authors: Felix Meier, Daniel Waltner, Petr Braun, Thomas Guhr
• Abstract summary: We derive a formalism to express the spin algebra $mathfraksu(2)$ in a spin $s$ representation. We consider a system of $L$ fermion flavors and apply our mapping in order to express it in terms of the spin algebra.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive a formalism to express the spin algebra $\mathfrak{su}(2)$ 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.

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