I am working on PDE. Recently I have been studying magnetic Sobolev spaces. While the theory is clear to me, having very little knowledge about physics, I have almost no idea how these spaces help while dealing with some physics problem.
More precisely, I want to know some situations when the operator $\nabla +iA$ comes into picture in physics. Can you suggest some books/notes where these things are explained using very less physics? I mean, it would be great if the intended readers of those notes/book are students of mathematics and not of physics.
Thank you in advance.