Off-shell dynamics of the O(3) NLS model beyond Monte Carlo and perturbation theory

The off-shell dynamics of the O(3) non-linear sigma model is probed in terms of spectral densities and two-point functions by means of the form factor approach. The exact form factors of the spin field, Noether current, EM tensor and the topological charge density are computed up to six particles. The corresponding n less than or equal to 6 particle spectral densities are used to compute the two-point functions, and are argued to deviate at most a few per mille from the exact answer in the entire energy range below 10(3) in units of the mass gap. To cover yet higher energies we propose an extrapolation scheme to arbitrary particle numbers based on a novel scaling hypothesis for the spectral densities. It yields candidate results for the exact two-point functions at all energy scales and allows us to exactly determine the values of two, previously unknown, non-perturbative constants. (C) 1997 Elsevier Science B.V.