Symmetry Under $α\rightarrow α+ 1$ is Forbidden by Helicity Conservation

Abstract

The question as to whether helicity conservation in spin one-half Aharonov Bohm scattering is sufficient in itself to determine uniquely the form of the spinor wave function near the origin is examined. Although it is found that a one parameter family of solutions is compatible with this conservation law, there must nonetheless be singular solutions which break the symmetry $α\rightarrow α+1$ required for an anyon interpretation. Thus the free parameter which occurs does not allow one to eliminate the singular solutions even though it does in principle mean that they can be transferred at will between the spin up and spin down configurations.