2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149173We construct a two dimensional nonlinear $σ$-model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear $σ$-model by the Hamiltonian flow. We use localization methods to evaluate the corresponding partition function for a general class of integrable systems, and find relations that can be viewed as generalizations of standard relations in classical Morse theory.essentially revised, 18 pages, latex (run twice)High Energy Physics - Theorytext