Feynman path integrals and Lebesgue–Feynman measures

Feynman path integrals on phase space and the metaplectic representation

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 integrals and motives

This article gives an overview of recent results on the relation between quantum field theory and motives, with an emphasis on two different approaches: a “bottom-up” approach based on the algebraic geometry of varieties associated to Feynman graphs, and a “top-down” approach based on the comparison of the properties of associated categorical structures. This survey is mostly based on joint wor...

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 ...