  We investigate the extension of the Prokof'ev-Svistunov worm algorithm to
Wilson lattice fermions in an external scalar field. We effectively simulate by
Monte Carlo the graphs contributing to the hopping expansion of the two-point
function on a finite lattice to arbitrary order. Tests are conducted for a
constant background field i. e. free fermions at some mass. For the method
introduced here this is expected to be a representative case. Its advantage is
that we know the exact answers and can thus make stringent tests on the
numerics. The approach is formulated in both two and three space-time
dimensions. In D=2 Wilson fermions enjoy special positivity properties and the
simulation is similarly efficient as in the Ising model. In D=3 the method also
works at sufficiently large mass, but there is a hard sign problem in the
present formulation hindering us to take the continuum limit.
