Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry
High Energy Physics - Theory
2008-11-26 v2
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.
Cite
@article{arxiv.0710.5178,
title = {Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry},
author = {Paul K. Townsend},
journal= {arXiv preprint arXiv:0710.5178},
year = {2008}
}
Comments
21 pages. Revised to include improved discussion of qantum theory and additional references