In this paper http://www.hcs.harvard.edu/~jus/0302/song.pdf when Song was explaining dirac string. He said "In the presence of a magnetic monopole, the vector potential cannot be defined everywhere. Thus, to describe the physics of magnetic monopoles, we must use two vector potentials A1 and A2 which are related by a transformation."
Why is it that we must use (at least) 2 vector potentials?
And in what way are they related by a transformation? (P. 52 on the right hand side column)
