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Communications in Theoretical Physics

A Hybrid Mapping of an Odd Fermion System and Many-Body Forces

Pan Ji-zhi, Wang Ru-lin, Bao Cheng-guang

Published Dec 1, 1986• 0 citations
Publisher

Abstract

In this paper, we derive a boson-fermion hybrid representation for the antisymmetrizer, and obtain an exact mapping of the fermion space onto a hybrid space. The results show that the effect of the antisymmetrizer appears as different kinds of many body forces among the bosons and the fermion.
DOI
10.1088/0253-6102/6/4/357

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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.