Invariant Imbedding and Mathematical Physics. I. Particle Processes

Abstract

With the use of invariance principles in a systematic fashion, we shall derive not only new analytic formulations of the classical particle processes, those of transport theory, radiative transfer, random walk, multiple scattering, and diffusion theory, but, in addition, new computational algorithms which seem well fitted to the capabilities of digital computers. Whereas the usual methods reduce problems to the solution of systems of linear equations, we shall try to reduce problems to the iteration of nonlinear transformations. Although we have analogous formulations of wave processes, we shall reserve for a second paper in this series a detailed and extensive treatment of this part of mathematical physics.