  We derive an exact representation of the massless Schwinger model on the
lattice in terms of dual variables which are configurations of loops, dimers
and plaquette occupation numbers. When expressed with the dual variables the
partition sum has only real and positive terms also when a chemical potential
or a topological term are added -- situations where the conventional
representation has a complex action problem. The dual representation allows for
Monte Carlo simulations without restrictions on the values of the chemical
potential or the vacuum angle.
