GENERALIZED VECTOR MEASURES AND FEYNMAN PATH INTEGRALS

Ludwig Streit, T. HIDA

Виктор Павлович Маслов, Alexander Mikhailovich Chebotarev

Richard J. Creswick

A method for numerically evaluating Feynman path integrals based on the density of actions is presented. The method is illustrated by calculating the propagator for the free particle and the simple harmonic oscillator.

Luiz C. L. Botelho

We show that Nelson's stochastic mechanics suitably formulated as a Hamilton–Jacobi first-order equation leads straightforwardly to the Feynman path integral formulation of quantum mechanics.

Sergio A Albeverio, Raphael J. Høegh-Krohn

Sergio A Albeverio, Giuseppina Guatteri, Sonia Mazzucchi

The Belavkin equation, describing the continuous measurement of the momentum of a quantum particle, is studied. The existence and uniqueness of its solution is proved via analytic tools. A stochastic characteristics method is applied. A rigorous representation of the solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the phase space is also given.