Speaker
Description
$3+1$ dimensional QED with massless electrons is chirally symmetric, at least in the perturbative regime. This is true, even though this symmetry is anomalous, because QED lacks instantons. However, in the presence of external magnetic fields, approximate calculations based on Schwinger-Dyson equations indicate that chiral symmetry is spontaneously broken. In a constant external magnetic field $B$, this produces a dynamical electron mass $\propto\sqrt{eB}$ and a chiral condensate $\propto(eB)^{3/2}$. The magnetic field catalyses chiral symmetry breaking with an effective dimensional reduction from $3+1$ dimensions to $1+1$ dimensions. We simulate lattice QED in a constant homogeneous magnetic field using the RHMC algorithm. We increase $\alpha$ from $1/137$ to $1/5$ to make the chiral symmetry breaking measurable. To access the chiral limit, we need to increase the lattice size. By using a large $eB$, the localization of the motion in the plane perpendicular to the magnetic field due to the dominance of low lying Landau levels means that we only need a large lattice size in the directions of $B$ and time. Our preliminary `data' show clear evidence for a non-zero condensate in the zero electron mass limit and hence chiral symmetry breaking.
