Reduction of self-dual yang-mills equations with respect to subgroups of the extended poincaré group

Abstract

For the vector potential of the Yang-Mills field in the Minkowski space R(1, 3), we construct the ansatze that are invariant under three-parameter subgroups of the extended Poincare group\(\tilde P\)(1, 3). We perform the symmetry reduction of self-dual Yang-Mills equations to systems of ordinary differential equations.