I am developing a computer simulation of the Ginzburg-Landau model of superconductivity. In a few words, I have discretized the domain with finite differences and I am using Nonlinear Conjugate Gradient Descent to find the solution.
However, I am not sure of how to deal with gauge invariance. What is the best practice? Should I avoid gauge fixing or should I assume Coulomb gauge for example?
Since without gauge fixing I would find multiple field configurations with the same energy, I guess gauge fixing is the way to go. Is this correct?