correction it's 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 don't have the energy to write a clear explanation of this for people who don't 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 i'll be amazed if this correction actually shows up i 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