Hidden algebra of the $N$-body Calogero problem

Details Hidden algebra of the $N$-body Calogero problem Hidden algebra of the $N$-body Calogero problem

1993-10-19

arxiv.org/abs/hep-th/9310125v2

Phys.Lett. B320 (1994) 281-286

Physics

High Energy Physics

High Energy Physics - Theory

10pp., CWRU-Math, October 1993

Scientific paper

10.1016/0370-2693(94)90657-2

A certain generalization of the algebra $gl(N,{\bf R})$ of first-order differential operators acting on a space of inhomogeneous polynomials in ${\bf R}^{N-1}$ 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. Given representation 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 above algebra. This representation is an alternative to the standard representation of the Bargmann-Fock type in terms of creation and annihilation operators.

Affiliated with

Also associated with

No associations

Rating

Hidden algebra of the $N$-body Calogero problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hidden algebra of the $N$-body Calogero problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hidden algebra of the $N$-body Calogero problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-262320