In QFT, given a gauge group and matter field, is the form of the gauge field unique? In other words, given a principal G-bundle and its associated vector bundle, is the construction of the principle G-connection unique?
This is related to the other question (here: Gauge Field Tensor from Wilson Loop) where the author implies that the gauge field is natural/unique given the matter field. May be it is, but I wanted to confirm (edit: From answer below, the gauge connection is not unique)
Because a gauge connection (or a gauge field) can exist independent of the vector matter field (as in pure gauge theories), non-uniqueness of the connection would imply a symmetry on the connection itself.