Yang–Mills theory in null-path space

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Abstract
We define a GL(n,C) matrix-valued function G on a six-dimensional space of null paths in Minkowski space. Such paths are defined to begin at an arbitrary spacetime point xa and end at future null infinity. The space of these paths can thus be parametrized by giving the point xa and null direction. We show how knowledge of G can be used to obtain the GL(n,C) Yang–Mills connection at xa. We also derive a single equation for G, involving characteristic data given on null infinity, which is equivalent to the currentless or vacuum Yang–Mills field equations. The self-dual (anti-self-dual) nonabelian fields and the general abelian cases are described as special examples.

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