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We simulate QED in a strong constant homogeneous external magnetic field on aeuclidean space-time lattice using the Rational Hybrid Monte Carlo method,developed for simulating lattice QCD. Our primary goal is to measure the chiralcondensate in the limit when the input electron mass $m$ is zero. We observe anon-zero value, indicating that the external magnetic field catalyzes chiralsymmetry breaking as predicted by approximate truncated Schwinger-Dysonmethods. Such behaviour is associated with dominance by the lowest Landau levelwhich causes the effective dimensional reduction from $3+1$~dimensions to $1+1$dimensions for charged particles (electrons and positrons) where the attractiveforces of QED can produce chiral symmetry breaking with a dynamical electronmass and associated chiral condensate. Since our lattice simulations use bare(lattice) parameters, while the Schwinger-Dyson analyses work with renormalizedquantities, direct numerical comparison will require renormalization of ourlattice results.

Lattice QED in an external magnetic field: Evidence for dynamical chiral symmetry breaking