What's the meaning of spin in 1+1 spacetime?

[ingenue]

When people discuss the Schwinger model, sometimes they still call the electron field spin-1/2 and the EM field spin-1. I wonder if there's some justification for these calling, since there's no rotations at all in 1+1 spacetime. I know for SO(n) with n>=2, one can always have well-defined spins.

 

[tom.stoer]

In 1+1 dim. the spin comes from the SO(1,1) Lorentz group. There are two-component spinors, a gamma matrix representation can be constructed from the Pauli matrices.

Of course there is no rotation in the ordinary sense, but the mathematics underlying spin is similar to the 3+1 dim case.