Consider, for example, the implication this has for plane rotations. Rotating a vector through an angle of θ corresponds to γ = exp(θ σ 1 σ 2), so that the corresponding action on spinors is via γ = ± exp(θ σ 1 σ 2 /2). In general, because of logarithmic branching, it is impossible to choose a sign in a consistent way. Thus the representation of plane rotations on spinors is two-valued.