Hidden algebra of the N-body Calogero problem |
| |
Authors: | Alexander Turbiner |
| |
Affiliation: | Mathematical Department, Case Western Reserve University, Cleveland, OH 44106, USA |
| |
Abstract: | A certain generalization of the algebra gl(N, ) of first-order differential operators acting on a space of inhomogeneous polynomials in N−1 is constructed. The generators of this (non-) Lie algebra depend on permutation operators. It is shown that the Hamiltonian of the N-body Calogero model can be represented as a second-order polynomial in the generators of this algebra. The representation given implies that the Calogero Hamiltonian possesses infinitely-many finite-dimensional invariant subspaces with explicit bases, which are closely related to the finite-dimensional representations of the above algebra. This representation is an alternative to the standard representation of the Bargmann-Fock type in terms of creation and annihilation operators. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|