Abstract
A two-loop effect, uncovered by Scharnhost, causes both the phase and the group velocities of electromagnetic waves with ω ⪡ m e to exceed c, when the wave is travelling between parallel conducting plates. We begin an analysis of the structure of the one-loop four-point function in flat space (this operator is used in the construction of the two-loop vacuum polarization function) that ensures the non-trivial dependence on frequency of both the effective action and the refractive index. Including corrections due to boundaries, this operator leads to the vanishing asymptotic behaviour of the vacuum polarization function which, contrary to the suggestion of Scharnhost and Barton, avoids the propagation of non-causal signals.
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