Breakdown of Microcausality for QFT in Curved Spacetime

by Tim Hollowood (Univ. Swansea, UK)

Tuesday 14 Aug 2007, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

We show that QED in curved spacetime violates micro-causality, i.e. commutators of fields at spacelike separations do not vanish but exhibit a characteristic exponential fall-off over a length scale R^{1/2}/m^2, where R is a typical curvature and m is the electron mass. The violation of micro-causality is ultimately related to the generic focusing nature of congruences of geodesics in curved spacetime, as implied by the null energy condition, and the existence of conjugate points. These results arise from a calculation of the complete non-perturbative frequency dependence of the vacuum polarization tensor in QED, using novel world-line path integral methods together with the Penrose plane-wave limit of spacetime in the neighbourhood of a null geodesic. The refractive index of curved spacetime is shown to exhibit superluminal phase velocities, dispersion, absorption (due to gamma to e^+e^-) and bi-refringence, but we demonstrate that the wavefront velocity (the high-frequency limit of the phase velocity) is indeed c, thereby guaranteeing that causality itself is respected. These effects will be generic for any QFT in curved spacetime and must have a significant impact on any quantum theory of gravity.