Path-Integral Approach to Classical Mechanics
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In this talk we review the path-integral approach to classical Hamiltonian dynamics (CM) recently proposed. This formulation brings to light a set of hidden (BRS-like) symmetries connected with the symplectic geometry of CM. We also explore some further universal hidden symmetries related to the dynamics of the system. These new invariances have the character of a genuine supersymmetry. We show that dynamical systems with this supersymmetry unbroken are ergodic. KAM systems and systems with few constants of motion beside the energy (and even integrable ones) have this supersymmetry spontaneously broken. In the conclusion we present a new derivation of the KMS conditions based on this hidden supersymmetry.
KeywordsClassical Mechanic Classical Mechanic Gibbs State Algebraic Characterization Hamiltonian Vector Field
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