Cherenkov radiation and superluminal particles

Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the v a c u u m emit Cherenkov radiation. How can a particle move faster than light? The w e a k speed of a charged particle can exceed the speed of light. By definition, the weak velocity is <b|v|a>/<b|a> where v is the velocity operator and |a> and |b> are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that superluminal weak speed is consistent with relativistic causality.