# Lepton flavor violation in QED?

QED strictly preserves lepton flavor violation. My question is: why is the operator such as

$$\bar{\mu}_L \gamma^\mu(\partial_\mu - iqA_\mu) e_R$$

not allowed in QED? Supposing the kinetic term for electron and muon are already included. So this operator is not an off-diagonal kinetic. It is also gauge invariant and renormalizable (mass dimension = 4). What forbids it?

• you must mean lepton number is conserved in QED – anna v Apr 22 '17 at 5:32