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  )