  We propose a four-dimensional interpretation of the outgoing state of the
scattering of a massless fermion off a Dirac monopole. It has been known that
such a state has fractional fermion numbers and is necessarily outside the Fock
space on top of ordinary perturbative vacuum, when more than two flavours of
charged Dirac fermions are considered. In this paper, we point out that the
Fock space of the fermions depends on the rotor degree of freedom of the
monopole and changes by a monopole-fermion s-wave scattering. By uplifting the
fermion-rotor system introduced by Polchinski, from two to four dimensions, we
argue that the outgoing state can be understood as a state in a different Fock
space.
