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Supersymmetry in hydrodynamics: vorticity as a ghost charge

Abstract
The path-integral approach to classical Hamiltonian dynamics (i.e. the functional-integral representation of classical transition probabilities), recently developed by Gozzi, is applied for studying the perfect fluid. In this way, by studying the symplectic structure of volume-preserving diffeomorphism the Thompson circulation theorem is shown to be equivalent to the conservation of ghost charge - one of the generators related to the (graded) ISp(2) symmetry present in any Hamiltonian system.