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arXiv:1001.0274 · Annals of Physics

Bosons, fermions and anyons in the plane, and supersymmetry

P. A. Horváthy, Mikhail S. Plyushchay, Mauricio Valenzuela

Published Apr 11, 2010• 74 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2010.02.007

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We argue that fermion-boson mapping techniques represent a natural tool for studying many-body supersymmetry in fermionic systems with pairing. In particular, using the generalized Dyson mapping of a many-level fermion superalgebra with the SU(2) type of pairing we investigate two kinds of supersymmetry connecting excitations in the systems with even and odd particle numbers: dynamical supersymmetry, which ensures a unified classification of states for both even and odd populations, and invariant supersymmetry with actual degeneracies of states within the same supermultiplet. Dynamical supersymmetries based on the dynamical algebra of the type $\mathrm{U}(K∕2\ensuremath{\Omega})$ (where KKK and $2\ensuremath{\Omega}$ denote the number of fermion-pair and single-fermion states, respectively) naturally arise in the bosonized description of the system. Conditions for invariant supersymmetry are determined in a restricted case of bilinear supercharge operators.