  Magnetars are surrounded by diffuse plasma in magnetic field strengths well
above the quantum electrodynamic critical value. We derive equations of
"quantum force-free electrodynamics" for this plasma using effective field
theory arguments. We argue that quantum effects do not modify the large scale
structure of the magnetosphere, and in particular that the spin-down rate does
not deviate significantly from the classical result. We provide definite
evolution equations that can be used to explore potentially important
small-scale corrections, such as shock formation, which has been proposed as a
mechanism for both burst and quiescent emission from magnetars.
