Michel Devoret " Brian Josephson's Gauge- Invariant Phase Difference: Should we view it as an angle or a position on an open line ? - Shared screen with speaker view
I am sorry I have to hop off for another meeting. I meant to push it back by 30 mins but it just slipped off my mind.
This works for x and p too (but there it can be non-integer)
Yes. Think of N as angular momentum. It has integer eigenvalues. The corresponding rotor eigenfunctions are e(in theta). If you multiply e^(in theta) by e^(ik theta) you raise the angular momentum by k units