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Explicit Solution to the N-Body Calogero Problem | | L. Brink
; T.H. Hansson
; M.A. Vasiliev
; | | Date: |
11 Jun 1992 | | Journal: | Phys.Lett. B286 (1992) 109-111 | | Abstract: | We solve the N-body Calogero problem, ie N particles in 1 dimension subject to a two-body interaction of the form $half sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $ a_i^mp =frac 1 {sqrt 2} (x _i pm ihat{p}_i )$, where $hat{p}_i$ is a modified momentum operator obeying %!!!!!!! Heisenberg-type commutation relations with $x_i$, involving explicitly permutation operators. On the other hand, $ D_j =i,hat{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. | | Source: | arXiv, hep-th/9206049 | | Services: | Forum | Review | PDF | Favorites | |
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