I posted this here because gauges seem to play a far more significant role in modern physics than in classical (bar the obvious exceptions). I want to ask a general question: I've been reading about gauges and gauges theories recently, but nowhere have I actually found solid justification for/reasoning as to why these gauges were introduced. For example, is the use of the Lorenz gauge in (classical) electromagnetism merely a device so that the vector and scalar potentials can be expressed in the form of homogenous wave equations? This question basically summarises what I am wondering - why a particular gauge? If anyone could shed some more light on what appears in most of the literature I have consulted to have been introduced in an ad hoc manner with no justification, I would be grateful; thank you.