Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry
classification
✦ hep-th
keywords
generalhamilton-jacobimechanicspseudo-supersymmetryrelationsystemconditioncosmology
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For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is the `BPS' condition for preservation of 1/2 pseudo-supersymmetry. The examples of the relativistic and non-relativistic particle, in a general potential, are worked through in detail, and used to discuss the relation to cosmology and to supersymmetric quantum mechanics.
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