Angular Smoothing and Spatial Diffusion from the Feynman Path Integral Representation of Radiative Transfer
Journal of Quantitative Spectroscopy and Radiative Transfer
The propagation kernel for time dependent radiative transfer is represented by a Feynman Path Integral (FPI). The FPI is approximately evaluated in the spatial-Fourier domain. Spatial diffusion is exhibited in the kernel when the approximations lead to a gaussian dependence on the Fourier domain wave vector. The approximations provide an explicit expression for the diffusion matrix. They also provide an asymptotic criterion for the self-consistency of the diffusion approximation. The criterion is weakly violated in the limit of large numbers of scattering lengths. Additional expansion of higher-order terms may resolve whether this weak violation is significant.