Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-02-07
Nucl.Phys. B401 (1993) 591-612
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, Latex, USITP-92-14, G{\"o}teborg ITP-92-53
Scientific paper
10.1016/0550-3213(93)90315-G
We discuss several applications and extensions of our previous operator solution of the $N$-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$. Using a complex representation of the deformed Heisenberg algebra underlying the Calogero model, we explicitly establish the equivalence between this system and anyons in the lowest Landau level. A construction based on supersymmetry is used to extend our operator method to include fermions, and we obtain an explicit solution of the supersymmetric Calogero model constructed by Freedman and Mende. We also show how the dynamical $OSp(2;2)$ supersymmetry is realized by bilinears of modified creation and annihilation operators, and how to construct a supersymmetic extension of the deformed Heisenberg algebra.
Brink Lars
Hansson T. H.
Konstein S.
Vasiliev Mikhail A.
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