  We consider the Lorentz contraction of a fermion-antifermion bound state in
1+1 dimensional QED. In 1+1 dimensions the absence of physical, propagating
photons allows us to explicitly solve the weak coupling limit \alpha << m^2 of
the Bethe-Salpeter bound state equation in any Lorentz frame. In a time-ordered
formalism it is seen that all pair production is suppressed in this limit. The
wave function is shown to contract while the mass spectrum is invariant under
boosts.
