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