Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry
arXiv:0710.5178 · doi:10.1088/0264-9381/25/4/045017
Abstract
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.
21 pages. Revised to include improved discussion of qantum theory and additional references