The internal symmetry group of a connection on a principal fiber bundle with applications to gauge field theories

The internal symmetry group of a connection on a principal fiber bundleP is studied. It is shown that this group is a smooth proper Lie transformation group ofP, which, ifP is connected, is also free. Moreover, this group is shown to be isomorphic to the centralizer of the holonomy group of the connection. Several examples and applications of these results to gauge field theories are given.