The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index

TL;DR

This paper investigates how vacuum polarization affects photon propagation in curved spacetime within scalar QED, revealing a novel analytic structure that maintains causality but challenges traditional dispersion relations.

Contribution

It provides a compact formula for the frequency-dependent refractive index in curved spacetime and explores its implications for causality and photon amplification.

Findings

Refractive index depends on Van Vleck-Morette matrix and Penrose limit.

Superluminal propagation is consistent with causality.

Photon amplification can occur in curved spacetime.

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.