Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry

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

References in corpus (17)

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• Supergravity Domain Walls
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Cited by in corpus (19)

• First Order Description of D=4 static Black Holes and the Hamilton-Jacobi equation
• Integrable cosmological models with non-minimally coupled scalar fields
• Fake Superpotential for Large and Small Extremal Black Holes
• Reconstruction Procedure in Nonlocal Cosmological Models
• Reconstruction of Scalar Potentials in Modified Gravity Models
• A first-order formalism for timelike and spacelike brane solutions
• Fake supersymmetry versus Hamilton-Jacobi
• Superpotential method for chiral cosmological models connected with modified gravity
• Supersymmetry and Gravitational Duality
• Cosmological rotating black holes in five-dimensional fake supergravity
• BPS and non-BPS kinks in a massive non-linear S^2-sigma model
• Superpotential method for $F(R)$ cosmological models
• Superpotential method and the amplification of inflationary perturbations
• Fake supersymmetry with tadpole potentials
• Comments on fake supersymmetry
• Canonical D = 1 supergravity framework for FLRW cosmology
• New Integrable Chiral Cosmological Models with Two Scalar Fields
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity
• Domain Walls in AdS-Einstein-scalar Gravity