Lattice QED in external electromagnetic fields

We study QED in external electromagnetic fields using methods developed for simulating lattice QCD. Our first project is to simulate QED in a constant (in space and time) external magnetic field on a euclidean space-time lattice using the Rational Hybrid Monte Carlo (RHMC) method. Observables we measure include the condensate $\langle\bar{\psi}\psi\rangle$ and the effective electron action after integrating out the fermion fields. We look for evidence that the combined effect of the magnetic field and the electron-positron attraction from QED produces a non-zero condensate in the limit of zero electron mass, a non-perturbative effect analogous to spontaneous chiral symmetry breaking. Very preliminary evidence is that such a condensate exists, at least for strong external magnetic fields and unphysically large electric charge. In addition, we are storing field configurations to measure the expected distortions and screenings of the coulomb field of a charged particle due to the vacuum polarization asymmetries produced by the magnetic field. We hope also to measure the dynamical contribution to the electron mass produced by the same mechanism that produces a finite condensate in the zero input mass limit.