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Superluminal Propagation Caused by Radiative Corrections in a Uniform Electromagnetic Field

We consider the effect of radiative corrections on the maximum velocity of propagation of neutral scalar fields in a uniform electromagnetic field. The propagator of neutral scalar fields interacting with charged fields depends on the electromagnetic field through charged particle loops. The kinetic terms of the scalar fields are corrected and the maximum velocity of the scalar particle becomes greater or less than unity. We show that the maximum velocity becomes greater than unity in a simple example, a neutral scalar field coupled with two charged Dirac fields by Yukawa interaction. The maximum velocity depends on the frame of reference and causality is not violated. We discuss the possibility of this superluminal propagation in the Standard Model.