Abstract
It is shown that in an algebraically special space-time that admits a congruence of null strings, the Yang–Mills equations with sources reduce to a pair of nonlinear first-order differential equations for two matrices, provided that the gauge field is aligned with the congruence. In the case where the current is tangent to the null strings, the gauge field is determined by a matrix potential that has to satisfy a second-order differential equation with quadratic nonlinearities. As an example of this case, the Yang–Mills–Weyl equations are reduced, assuming that the multiplet of Weyl neutrino fields are also aligned with the congruence, and a reduced form of the Einstein–Yang–Mills–Weyl equations is also given.
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