Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond Monte-Carlo and Perturbation Theory

TL;DR

This paper uses the form factor approach to analyze the off-shell dynamics of the O(3) nonlinear sigma-model, providing precise spectral densities and two-point functions beyond traditional Monte Carlo and perturbation methods.

Contribution

It introduces an extrapolation scheme for spectral densities at high energies and determines two previously unknown non-perturbative constants.

Findings

Spectral densities computed up to 6 particles deviate minimally from exact results.

Proposed extrapolation scheme extends results to arbitrary energies.

Exact values of two non-perturbative constants are determined.

Abstract

The off-shell dynamics of the O(3) nonlinear 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 6-particles. The corresponding $n\leq 6$ 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.