Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry

Details Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry

2007-10-26

arxiv.org/abs/0710.5178v2

Class.Quant.Grav.25:045017,2008

Physics

High Energy Physics

High Energy Physics - Theory

21 pages. Revised to include improved discussion of qantum theory and additional references

Scientific paper

10.1088/0264-9381/25/4/045017

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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