Feynman path integrals as analysis on path space by time slicing approximation

On the approximation of Feynman-Kac path integrals

The symbol D [x (τ)] indicates that the integration is performed over the set of all differentiable curves, x : [0, βh̄]→ R, with x (0) = a and x (βh̄) = b. The integer d reflects the dimensionality, with d = 3N for a system of N -particles in 3-dimensional space. The functional Φ can be derived from the classical action by introducing a relationship between temperature and imaginary time (it = β...

Feynman path integrals on phase space and the metaplectic representation

Approximation Solutions for Time-Varying Shortest Path Problem

Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

Systematic Upscaling for Feynman Path Integrals A Progress Report

The path integral approach was introduced by Feynman in his seminal paper (Feynman, 1948). It provides an alternative formulation of time-dependent quantum mechanics, equivalent to that of Schrödinger. Since its inception, the path integral has found innumerable applications in many areas of physics and chemistry. The reasons for its popularity are numerous. First, the path integral formulation...

Beam spread functions calculated using Feynman path integrals

A method of solving the radiative transfer equation using Feynman path integrals (FPIs) is discussed. The FPI approach is a mathematical framework for computing multiple scattering in participating media. Its numerical behavior is not well known, and techniques are being developed to solve the FPI approach numerically. A missing numerical technique is detailed and used to calculate beam spread ...