Projective unitary representation
= Projective unitary representation
Because state vectors differing by a <quantum phase> represent the same ray, a unitary realization of a group action need only satisfy
$$
U(g_1)U(g_2)=e^{i\phi(g_1,g_2)}U(g_1g_2).
$$
A <projective unitary representation> is a <projective representation> whose chosen representatives are unitary operators. The phase factors disappear on rays.