Causality in the Fermi Problem and the Magnus expansion

Abstract

In 1932, Fermi presented a two-atom model for determining whether quantum mechanics is consistent with causality, and concluded that indeed it is. In the late 1960's, Shirokov and others found that Fermi's approximations may not have been sound, and when corrected, Fermi's model shows non-causal behavior. We show that if instead of time-dependent perturbation theory, the Magnus expansion is used to approximate the time-evolution operator, causality does follow.