It is assumed that a valid QFT, must have states/observables in a Hilbert space, transform according to the projective unitary representations of the Poincare group.
I can understand why the observables must transform according to unitary representations of the Poincare group, but don't see any compelling reason for that symmetries must be projective as well.
Some have explained it, as it is required for dealing with the phase factor redundancy in the wavefunction,but I guess this redundancy is dealt by the unitary representation itself, as the phase factors cancels out. I don't see why a phase factor redundancy demands the symmetry be projective.
