Algebra of one-particle operators for the Calogero model Original Research Article

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