2007/07/31 by Timothy J. Hollowood, G.M. Shore, Graham M. Shore · 5 citations
Physics and Astronomy · #Advanced Fiber Laser Technologies #Black Holes and Theoretical Physics #Quantum Electrodynamics and Casimir Effect #gr-qc #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.11.034
published as Nucl.Phys.B795:138-171,2008 · 43 pages, 19 figures, JHEP3, conclusions respecting microcausality modified
arxiv created 2007/10/29 · openalex publication_date 2007/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.