arXiv 0707.23022007-07hep-thgr-qc

弯曲时空中的因果性与微观因果性

Causality and Micro-Causality in Curved Spacetime

Timothy J. Hollowood, Graham M. Shore

备注：: 16 pages, 11 figures, JHEP3, microcausality now shown to be respected even when the Kramers-Kronig relation is violated
发表信息：: Phys.Lett.B655:67-74,2007
DOI：: 10.1016/j.physletb.2007.08.073

摘要：

我们考虑如何实现因果关系和微观因果关系在QED弯曲时空。光子传播子被发现表现出新的非解析行为，由于真空偏振，这使Kramers-Kronig色散关系失效，并质疑弯曲时空中微观因果关系的有效性。这种非解析性最终与弯曲时空中测地线的汇点的一般聚焦性质有关，这是由零能量条件和共枕点的存在所暗示的。这些结果产生于一个完整的非微扰的QED真空极化张量的频率依赖性的计算，使用新的世界线路径积分方法连同时空的彭罗斯平面波极限在一个零测地线附近。弯曲时空的折射率表现出超光速的相速度、色散、吸收（由于γ \to e^+e^-）和双折射，但我们证明波前速度（相速度的高频极限）确实是c，从而保证因果关系本身得到尊重。

英文摘要：

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. The refractive index of curved spacetime is shown to exhibit superluminal phase velocities, dispersion, absorption (due to γ\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.

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