Scattering of Plane Waves in Self-Dual Yang-Mills Theory

TL;DR

This paper presents an exact solution for the scattering of multiple plane waves in self-dual Yang-Mills theory, introducing a scattering operator that simplifies the mathematical description of the process.

Contribution

It provides a novel exact solution and a compact operator formalism for describing plane wave scattering in self-dual Yang-Mills equations.

Findings

Exact solution for n-plane wave scattering

Introduction of a scattering operator $\uhat{T}$

Compact mathematical representation of scattering process

Abstract

We consider the classical self-dual Yang-Mills equation in 3+1-dimensional Minkowski space. We have found an exact solution, which describes scattering of $n$ plane waves. In order to write the solution in a compact form, it is convenient to introduce a scattering operator $\hat{T}$. It acts in the direct product of three linear spaces: 1) universal enveloping of $su(N)$ Lie algebra, 2) $n$-dimensional vector space and 3) space of functions defined on the unit interval.