Journal of the Korean Mathematical Society

FEYNMAN INTEGRALS, DIFFUSION PROCESSES AND QUANTUM SYMPLECTIC TWO-FORMS

Jean-Claude Zambrini

Published Jan 1, 2001• 6 citations

Abstract

This is an introduction to a stochastic version of E. Cartan's symplectic mechanics. A class of time-symmetric (Bern- stein) diusion processes is used to deform stochastically the ex- terior derivative of the Poincare-Cartan one-form on the extended phase space. The resulting symplectic two-form is shown to contain the (a.e.) dynamical laws of the diusions. This can be regarded as a geometrization of Feynman's path integral approach to quantum theory; when Planck's constant reduce to zero, we recover Cartan's mechanics. The underlying strategy is the one of Euclidean Quan- tum Mechanics.

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