The parallel propagator as basic variable for Yang-Mills theory

The parallel propagator (associated with a Yang-Mills connection) taken along all null geodesics from a field point x to null infinity is introduced as a basic variable in Yang-Mills theory. It is shown that the Yang-Mills connection can be reconstructed from this parallel propagator. The Yang-Mills equations are expressed as an equation for the parallel propagator. This equation can be given as a sum of two parts. The first of these, when set equal to zero on its own, satisfies the Huygens property and is soluble. When the second part is included, the Huygens property is destroyed. This leads to an approximation scheme which at first order is soluble yet already captures much of the non-linearity of Yang-Mills theory. (orig.)