Anyons in 1+ 1 dimensions are anomalous (original) (raw)

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. That is, the construction of a purely bosonic effective local theory starting from a system of bosons and fermions upon integration over the fermionic variables. We consider a quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation. It is found that, unless the flux enclosed by the particle orbits is quantized, and the spin takes a value n + 1/2, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously avoid the anomaly and force the particles to be