THE CALOGERO MODEL - ANYONIC REPRESENTATION, FERMIONIC EXTENSION AND SUPERSYMMETRY

被引:148
作者
BRINK, L
HANSSON, TH
KONSTEIN, S
VASILIEV, MA
机构
[1] UNIV STOCKHOLM,INST THEORET PHYS,S-11346 STOCKHOLM,SWEDEN
[2] PN LEBEDEV PHYS INST,DEPT THEORET PHYS,MOSCOW 117924,RUSSIA
关键词
D O I
10.1016/0550-3213(93)90315-G
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We discuss several applications and extensions of our previous operator solution of the N-body quantum-mechanical Calogero problem, i.e. N particles in one dimension subject to a two-body interaction of the form 1/2SIGMA(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.
引用
收藏
页码:591 / 612
页数:22
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