Sean Carroll is currently wrapping up a series of videos about the Biggest Ideas in the Universe. All of the usual hocus-pocus around quantum fields and quarks. The last (?) in this series – Idea No. 15 – is about gauge theories. It is one of those things: the multiplication of theoretical and mathematical concepts after WW II has been absolutely mind-boggling !
Any case, as an antidote, it is good to remind ourselves that – unlike other field theories (quantum field theories, to be precise) – we have one gauge only in electromagnetism – the Lorenz gauge – and it is not some weird metaphysical concept resulting from equally weird redundant degrees of freedom in our theory. No. The Lorenz gauge just pops when re-writing Maxwell’s equations in terms of four-vector potentials. That’s all. Nothing more, nothing less.
For a change, the Wikipedia article on it is very readable and straightforward: it also usefully links the unique (Lorenz) gauge for the QED sector to the concept of retarded potentials: traveling fields – and changes in static fields – travel at the speed of light. Any signal, in fact, will travel at the speed of light. We wrote about the implications of this in regard to de Broglie‘s concept of the matter-wave in earlier papers, so we will refer you there. 🙂
So should you or should you not invest in studying gauge theories? I don’t think so, but I’ll keep reading myself. I will keep you informed about what I learn (or not).