In quantum electrodynamics of two space dimensions, a quantum Hall
effect occurs in the absence of any magnetic field. We give a simple and
transparent explanation. In solid state physics, the Hall conductivity for
non-degenerate ground state is expected to be given by an integer, the
Chern number. In our field-free situation, however, the conductivity is
±1/2 in natural units. We fit this half-integral result into the topological
setting and give a geometric explanation reconciling the points of
view of quantum field theory (QFT) and solid state physics. For quasiperiodic
boundary conditions, we calculate the finite size correction to
the Hall conductivity. Applications to graphene and similar materials
are discussed.