THE CALOGERO MODEL - ANYONIC REPRESENTATION, FERMIONIC EXTENSION AND SUPERSYMMETRY

We discuss several applications and extensions of our previous operato r solution of the N-body quantum-mechanical Calogero problem, i.e. N p articles in one dimension subject to a two-body interaction of the for m 1/2SIGMA(i,j) [(x(i) - x(j))2 + g/(x(i) - x(j))2]. Using a complex r epresentation of the deformed Heisenberg algebra underlying the Caloge ro model, we explicitly establish the equivalence between this system and anyons in the lowest Landau level. A construction based on supersy mmetry is used to extend our operator method to include fermions, and we obtain an explicit solution of the supersymmetric Calogero model co nstructed by Freedman and Mende. We also show how the dynamical OSp(2; 2) supersymmetry is realized by bilinears of modified creation and an nihilation operators, and how to construct a supersymmetic extension o f the deformed Heisenberg algebra.