Variational treatment of quenched QED using the worldline technique

Perturbative Quantum Electrodynamics has been successfully tested to unparalleled precision for around half a century. In addition, and rather more recently, the theory’s behaviour in its strong coupling limit has attracted a growing amount of attention. 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 it 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. Traditionally, strongly coupled QED has been studied using Schwinger-Dyson, Lattice and renormalization group approaches. In this contribution we describe a rather different method, namely a variational approach using the worldline formulation of field theory. We have developed this technique in the context of a scalar field theory [1] and we applied it here, for the first time, to a gauge theory with spin2 particles. 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 bareand 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.