On the Characterization of Classical Dynamical Systems Using Supersymmetric Nonlinear $σ$-models

Details On the Characterization of Classical Dynamical Systems Using Supersymmetric Nonlinear $σ$-models On the Characterization of Classical Dynamical Systems Using Supersymmetric Nonlinear $σ$-models

1994-12-02

arxiv.org/abs/hep-th/9412023v4

Physics

High Energy Physics

High Energy Physics - Theory

essentially revised, 18 pages, latex (run twice)

Scientific paper

We construct a two dimensional nonlinear $\sigma$-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 $\sigma$-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.

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