GLOBAL ANOMALIES AND ANYONS IN 1+1-DIMENSIONS

We consider the analog in one spatial dimension of the Bose-Fermi tran smutation for planar systems. A quantum mechanical system of a spin 1/ 2 particle coupled to an abelian gauge field, which is classically inv ariant under gauge transformations and charge conjugation is studied. It is found that unless the flux enclosed by the particle orbits is qu antized, and the spin takes a value n + 1/2, at least one of the two s ymmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously force the particles to be either bosons or fermions, but not anyons. (C) 1997 Published b y Elsevier Science B.V.