FRACTIONAL SPIN FROM GRAVITY

Friedman and Sorkin have observed that the total angular momentum of a n asymptotically flat, vacuum, quantum gravitational field in 3+1 dime nsions need not be integral. We pursue this idea in the context of asy mptotically flat 2+1 gravity, which is an exactly solvable model. We f ind that, for nontrivial spatial topologies, the quantized pure gravit ational field has states of fractional spin. These states axe dynamica lly allowed, in the sense that they solve all the constraints of the t heory.