## Abstract

In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.

Original language | English (US) |
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Pages (from-to) | 3375-3388 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 37 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1996 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics