Abstract
Here we continue the study of the hidden symmetries revealed by the path-integral formulation of classical mechanics. We find that, besides the BRS and anti-BRS symmetry recently discovered, this formulation of classical mechanics presents a genuine supersymmetry associated to the energy conservation of the system. We prove that any dynamical system with this supersymmetry unbroken is ergodic. Moreover the supersymmetric invariant ground state turns out to be a Gibbs (and KMS) state. Systems with few constants of motion besides the energy (or even integrable systems) have this supersymmetry spontaneously broken but they present many more hidden graded symmetries besides the above-mentioned supersymmetry. These are symmetries associated to each constant of motion and each of them makes a S(2) superalgebra. For integrable systems this superalgebra is maximal and is S(2) n where n is the number of degrees of freedom of the system.
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