  We consider the possibility of using reweighting techniques in order to
correct for the breaking of unitarity when twisted boundary conditions are
imposed on valence fermions in simulations of lattice gauge theories. We start
by studying the properties of reweighting factors and their variances at
tree-level. That leads us to the introduction of a factorization for the
fermionic reweighting determinant. In the numerical, stochastic, implementation
of the method, we find that the effect of reweighting is negligible in the case
of large volumes but it is sizeable when the volumes are small and the twisting
angles are large. More importantly, we find that for un-improved Wilson
fermions, and in small volumes, the dependence of the critical quark mass on
the twisting angle is quite pronounced and results in large violations of the
continuum dispersion relation.
