The Refractive index of curved spacetime: The Fate of causality in QED
Jul, 2007Citations per year
Abstract: (Elsevier)
It has been known for a long time that vacuum polarization in QED leads to a superluminal low-frequency phase velocity for light propagating in curved spacetime. Assuming the validity of the Kramers–Kronig dispersion relation, this would imply a superluminal wavefront velocity and the violation of causality. Here, we calculate for the first time the full frequency dependence of the refractive index using world-line sigma model techniques together with the Penrose plane wave limit of spacetime in the neighbourhood of a null geodesic. We find that the high-frequency limit of the phase velocity (i.e. the wavefront velocity) is always equal to c and causality is assured. However, the Kramers–Kronig dispersion relation is violated due to a non-analyticity of the refractive index in the upper-half complex plane, whose origin may be traced to the generic focusing property of null geodesic congruences and the existence of conjugate points. This makes the issue of micro-causality, i.e. the vanishing of commutators of field operators at spacelike separated points, a subtle one in local quantum field theory in curved spacetime.- 04.62.+v
- 12.20.-m
- Quantum electrodynamics
- Curved space
- Causality
- Penrose limit
- Kramers-Kronig dispersion relation
- Kramers–Kronig dispersion relation
- quantum electrodynamics
- space-time
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