Algebra of one-particle operators for the Calogero model

Details Algebra of one-particle operators for the Calogero model Algebra of one-particle operators for the Calogero model

1995-10-25

arxiv.org/abs/hep-th/9510184v1

Nucl.Phys. B463 (1996) 194-214

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, LaTeX

Scientific paper

10.1016/0550-3213(96)00010-7

An algebra ${\cal G}$ of symmetric {\em one-particle} operators is constructed for the Calogero model. This is an infinite-dimensional Lie-algebra, which is independent of the interaction parameter $\lambda$ of the model. It is constructed in terms of symmetric polynomials of raising and lowering operators which satisfy the commutation relations of the $S_N$-{\em extended} Heisenberg algebra. We interpret ${\cal G}$ as the algebra of observables for a system of identical particles on a line. The parameter $\lambda$, which characterizes (a class of) irreducible representations of the algebra, is interpreted as a statistics parameter for the identical particles.

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