Yang-Mills fields on two-surfaces of constant curvature

A solution of the SL(2,R) Yang-Mills equations is described on a two-surface of constant negative curvature which is the analogue of the SU(2) Wu-Yang solution on S2. It represents the Maxwell field of a magnetic pole with a space-like geodesic world-line embedded in the SL(2,R) Yang-Mills theory. The corresponding 'pseudo-meron' solution is derived and is shown to be gauge related to one half the Maurer-Cartan form on SL(2,R) in the same way as the meron solution is gauge related to one half the Maurer-Cartan form on SU(2). (author)