The causal structure of QED in curved spacetime: analyticity and the refractive index

2008/06/30 by Timothy J. Hollowood, G.M. Shore, Graham M. Shore · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Causal structure #Classical mechanics #Cosmology and Gravitation Theories #Geodesic #Geodesics in general relativity #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Photon #Physics #Polarization (electrochemistry) #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum mechanics #Refractive index #Spacetime #Superluminal motion #Vacuum polarization #hep-th

paper · pdf · doi:10.1088/1126-6708/2008/12/091

published as JHEP 0812:091,2008 · 54 pages, 19 figures, corrected some signs in formulae and graphs

openalex publication_date 2008/12/22 · arxiv created 2011/11/10 · arxiv updated 2011/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.

Citations

• Covariant Perturbation Theory (IV). Third Order in the Curvature
• Quantum Fields in Curved Space
• Causality and micro-causality in curved spacetime
• Superluminality and UV completion
• Velocity of a signal in an attractive potential and propagation of light in a gravitational field
• The one-loop effective action and trace anomaly in four dimensions
• The refractive index of curved spacetime: The fate of causality in QED
• k-Essence, superluminal propagation, causality and emergent geometry
• Particle creation by black holes
• Faster-than-c Signals, Special Relativity, and Causality
• Microcausality in curved space-time
• The world as a hologram
• Causality, Analyticity and an IR Obstruction to UV Completion
• Dimensional Reduction in Quantum Gravity
• The Large Scale Structure of Space-Time
• Faster than light photons in gravitational fields II.

Cited by

• The refractive index of curved spacetime II: QED, Penrose limits and black holes
• The effect of gravitational tidal forces on vacuum polarization: How to undress a photon
• Asymptotic states and renormalization in Lorentz-violating quantum field theory
• Flavour effects in gravitational leptogenesis
• New non-linear modified massless Klein–Gordon equation
• Causality violation, gravitational shockwaves and UV completion