In the frame of Nelson stochastic quantization for dynamical systems on a manifold, we consider diffusion processes with Brownian covariance given by a Riemannian metric on the manifold. The dynamics is specified through a stochastic variational principle for a generalization of the classical action, with a given kinetic metric. The resulting programming equation, of the Hamilton-Jacobi type, depends on both metrics, the Brownian one and the kinetic one. We introduce a simple notion of compatibility between the two metrics, such that the programming equation and the continuity equation lead to the Schrödinger equation on the manifold. © 1985 The American Physical Society.
COMPATIBILITY BETWEEN THE BROWNIAN METRIC AND THE KINETIC METRIC IN NELSON STOCHASTIC QUANTIZATION / Daniela, Dohrn; Guerra, Francesco. - In: PHYSICAL REVIEW D. - ISSN 0556-2821. - 31:10(1985), pp. 2521-2524. [10.1103/physrevd.31.2521]
COMPATIBILITY BETWEEN THE BROWNIAN METRIC AND THE KINETIC METRIC IN NELSON STOCHASTIC QUANTIZATION
GUERRA, Francesco
1985
Abstract
In the frame of Nelson stochastic quantization for dynamical systems on a manifold, we consider diffusion processes with Brownian covariance given by a Riemannian metric on the manifold. The dynamics is specified through a stochastic variational principle for a generalization of the classical action, with a given kinetic metric. The resulting programming equation, of the Hamilton-Jacobi type, depends on both metrics, the Brownian one and the kinetic one. We introduce a simple notion of compatibility between the two metrics, such that the programming equation and the continuity equation lead to the Schrödinger equation on the manifold. © 1985 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.