Nuclear Physics B131 (1977) 525-546 © North-Holland Publishing Company ROTATIONALLY INVARIANT SOLUTIONS OF THE YANG-MILLS-HIGGS SYSTEM FOR A GENERAL GAUGE GROUP: MAGNETIC MONOPOLES P. CORDERO Departamento de Fisica, Facultad de Oencias Fisicas y Matemdticas, Universidad de Chile, Santiago Received 8 August 1977 (Revised 15 September 1977) A general form that the fields take in a spherically symmetric solution is derived from demanding that the field variables be spherically symmetric up to a local gauge transfor- mation. The gauge group is any compact, semisimple Lie group and the matter field • be- longs to a generic orthogonal representation of the gauge group. In this way the angular dependence of the field variables becomes explicit and new field variables are defined which depend just on r and t. Replacing this form of the field variables in the equations of motion we consider the static case and study some solutions. Of these we emphasize a f'mite-energy solution which generalizes both the monopole solution of 't Hooft and Polyakov and the dyon solution of Julia-Zee. The behaviour of the Yang-Mllls field near the origin is related to the "angular momentum" content of the adjoint representation of the gauge group while the corresponding behaviour of the Higgs field is related to the "angular momentum" content of the ~ representation. We have found a natural way to define the electromagnetic field of our finite-energy solution without requiring the matter field ~ to belong to the adjoint representation of the gauge group. It coincides with the 't Hooft prescription in the case considered by him. The magnetic charge of our solution is fixed. 1. Introduction The Yang-Mills-Higgs (YMH) system has proven to be richer than was originally thought; the presence of monopole-soliton type solutions came as a surprise [1 ]. In this paper we study two problems related to the monopole-soliton type of so- lutions of a YMH system having any n-parameter compact and semi-simple gauge Lie group. The scalar field transforms according to an unspecified m-dimensional or- thogonal representation of the gauge group. First, we study a general form that the fields take in a spherically symmetric so- lution. Secondly we study the dynamical problem of the spherically symmetric mo- tions and in particular we find the equations satisfied by the fields in the static case 525