The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics
Abstract
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the socalled Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, FeymanKaclike kernels are the building blocks for suitable transition probability densities of the process. In the standard "free" case (FeynmanKac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the "free noise" can also be extended to any infinitely divisible probability law, as covered by the LévyKhintchine formula. Since the relativistic Hamiltonians $\nabla $
 Publication:

arXiv eprints
 Pub Date:
 May 1995
 arXiv:
 arXiv:chaodyn/9505003
 Bibcode:
 1995chao.dyn..5003G
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 Latex file