,Vacuum polarization of scalar electrodynamics in flat space-time with nontrivial topology

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The one-loop vacuum polarization is calculated for scalar electrodynamics in a flat space-time with the topologyS1 ×R3. The effect of vacuum polarization upon photon propagation is considered. It is found that photon propagationbecomes anisotropic with some photon modes acquiring a positive topological mass and thus travelling at a subluminalspeed.
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