On the reality of the global phase

I respond to a recent argument by David Schroeren (Phil.Sci., forthcoming; philsci-archive.pitt.edu/20419/) that - contrary to a very wide consensus - global phase in quantum mechanics is real. I argue that Schroeren's argument rests on a mistaken assumption about projective representation theory and that, when this is corrected, the argument no longer follows. In doing so I give a brief introduction to projective representation theory