The Calogero model: Anyonic representation, fermionic extension and supersymmetry

Jan, 1993
24 pages
Published in:
  • Nucl.Phys.B 401 (1993) 591-612
e-Print:
Report number:
  • USITP-92-14,
  • GOTEBORG-92-53,
  • ITP-92-53

Citations per year

19932001200920172025024681012
Abstract:
We discuss several applications and extensions of our previous operator solution of the NN-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)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.
  • many-body problem
  • dimension: 1
  • algebra: representation
  • postulated particle: anyon
  • supersymmetry
  • fermion: operator
  • algebra: deformation