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 3rd 2005 Copied the above comment from Gauge theory since the relevant material is now in this article 76 167 77 165