Beam spread functions calculated using Feynman path integrals

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 ...

Phase Functions and Path Integrals

This note is an introduction to our forthcoming paper [17]. There we show how to construct the metaplectic representation using Feynman path integrals. We were led to this by our attempts to understand Atiyah’s explanation of topological quantum field theory in [2]. Like Feynman’s original approach in [9] (see also [10]) an action integral plays the role of a phase function. Unlike Feynman, we ...

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...

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...

Feynman path integrals on phase space and the metaplectic representation