Correction  Its not true that the sections of a principal bundle form a group  So this is  not a good definition of the group of gauge transformations  I was confused about this for a  long time myself  To get a group   you need the sections of the bundle associated to the principal bundle P by means  of the adjoint action of G on itself  I dont have the energy to write a clear explanation of this for people who dont know this sort of stuff  But I wanted to point out that the description of gauge transformations as sections of a principal bundle is wrong  Ill be amazed if this correction actually shows upI have no clue how Wiki works  Sorry   John Baez February rd   Copied the above comment from Gauge theory since the relevant material is now in this article