Explicit Solution to the N-Body Calogero Problem

1992/06/11 by Lars Brink, L. Brink, T. H. Hansson +2 · 16 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th

paper · pdf · doi:10.1016/0370-2693(92)90166-2

published as Phys.Lett. B286 (1992) 109-111 · 6 p., latex, USITP-92-5

arxiv created 1992/06/11 · openalex publication_date 1992/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form \half ∑_i,j[ (x_i - x_j)² + g/ (x_i - x_j)²], by constructing annihilation and creation operators of the form a_i^∓ =\frac 1 √ 2 (x _i ± ip_i ), where p_i is a modified momentum operator obeying %!!!!!!! Heisenberg-type commutation relations with x_i, involving explicitly permutation operators. On the other hand, D_j =i p_j can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed.

Citations

• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials

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