Related papers: Stochastic mechanics and the Feynman integral
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstien diagrams. We review recent results in…
In this paper, we consider stochastic Schroedinger equations with two-dimensional white noise. Such equations are used to describe the evolution of an open quantum system undergoing a process of continuous measurement. Representations are…
Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We…
We apply the recently developed theory of symmetry of stochastic differential equations to a stochastic version of the logistic equation, obtaining an explicit integration, i.e. an explicit formula for the process in terms of any single…
Previously suggested hidden time interpretation of quantum mechanics allows to reproduce the same predictions as standard quantum mechanics provides, since it is based on Feynman many - paths formulation of QM. While new experimental…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
I review the Feynman-Wiener path-integral formalism for diffusion with drift and jumps.
New physical insight into the correspondence between path integral concepts and the Schr\"odinger formulation is gained by the analysis of the effective classical potential, that is defined within the Feynman path integral formulation of…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark on Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden…
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The expectation values defined through path integrals obey Bell's inequalities in Euclidean time, but not in Minkowski time.…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
This essay explores the meaning of stochastic differential equations and stochastic integrals. It sets these subjects in a context of Riemann-Stieltjes integration. It is intended as a comment or supplement to \cite{MTRV}.
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion…