  Energy and momentum conservation in the context of a type II, purely
transmitting, defect, within a single scalar relativistic two-dimensional field
theory, places a severe constraint not only on the nature of the defect but
also on the potentials for the scalar fields to either side of it. The
constraint is of an unfamiliar type since it requires the Poisson Bracket of
the defect contributions to energy and momentum with respect to the defect
discontinuity and its conjugate to be balanced by the potential difference
across the defect. It is shown that the only solutions to the constraint
correspond to the known integrable field theories.
