Connection space approach to ambiguities of gauge theories

Two distinct gauge potentials can have the same field strength, in which case they are said to be “copies“ of each other. The consequences of this ambiguity for the general affine space 𝒜 of gauge potentials are examined. Any two potentials are connected by a straight line in 𝒜, but a straight line going through two copies either contains no other copy or is entirely formed by copies.