  There has been growing interest in studying the behaviour of QED in its
strong coupling limit. The reason for this is not only that it serves as a
simple prototype gauge theory for testing nonperturbative calculational
techniques which one then goes on to apply to QCD, but also because the theory
exhibits interesting behaviour in its own right. In particular, it now appears
to be quite well established that QED breaks chiral symmetry dynamically as
long as the coupling is sufficiently large. In this contribution we describe
the progress made in applying the polaron variational approach to quenched QED
within the context of the worldline formulation of field theory. Although it is
too early for quantitative results, qualitatively the approach seems promising:
The method is formulated covariantly in Minkowski space-time, the
Ward-Takahashi identities are satisfied, the connection between the bare- and
pole-masses of the electron is gauge independent, the known exact result for
the infrared dependence of the on-shell renormalized propagator is reproduced
and corrections to the variational approximation can be calculated
systematically.
