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DY: Fachverband Dynamik und Statistische Physik

DY 32: Posters DY - Statistical Physics, Brownian Motion and Nonlinear Dynamics

DY 32.17: Poster

Tuesday, March 23, 2021, 16:30–19:00, DYp

A Mapping between the Spin and Fermion Algebra — •Felix Meier, Daniel Waltner, Petr Braun, and Thomas Guhr — University Duisburg-Essen, Duisburg, Germany

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 expressing the fermionic operators of many-body systems as non-linear expressions 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)]. Then we 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 [1].

[1] arXiv:2101.10119 (2021)