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2007

Causality and Micro-Causality in Curved Spacetime

Hollowood, Timothy J., Shore, Graham M.

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We consider how causality and micro-causality are realised in QED in curved spacetime.

The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion relation and calls into question the validity of micro-causality in curved spacetime.
This non-analyticity 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.

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T.J. Hollowood and G.M. Shore, “The refractive index of curved spacetime: the fate of causality in QED,” arXiv:07072303 [hep-th]

Cited in the paper.

F. Bastianelli, arXiv:hep-th/0508205

Cited in the paper.

S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, “Microcausality in Curved Space-Time,” arXiv:0709.1483 [hep-th]

Cited in the paper.

T.J. Hollowood and G.M. Shore, in preparation

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