  The possible actions of symmetry groups on generalized Higgs fields coupled
to an Einstein-Yang-Mills field are studied with differential geometrical
techniques involving principal and associated bundles. A classification of
conjugacy classes of these actions and the form of the corresponding invariant
Einstein-Yang-Mills-Higgs (EYMH) fields is obtained and then applied to the
case of static spherically symmetric fields over four dimensional space-time.
The representations of the gauge group for which spherically symmetric Higgs
fields exist are identified and the set of all field equations for the
independent functions that describe these fields is analyzed and the
corresponding ordinary system of differential equations is derived and shown to
be consistent.
