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Causality and Micro-Causality in Curved Spacetime

Timothy Hollowood Orcid Logo, Graham Shore

Phys. Lett. B, Volume: 655, Pages: 67 - 74

Swansea University Authors: Timothy Hollowood Orcid Logo, Graham Shore

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DOI (Published version): 10.1016/j.physletb.2007.08.073

Abstract

It has been known for a long time that vacuum polarization in QED leads to a superluminal low-frequency phase velocity for light propagating in curved spacetime. Assuming the validity of the Kramers-Kronig dispersion relation, this would imply a superluminal wavefront velocity and the violation of c...

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Published in: Phys. Lett. B
Published: Elsevier 2007
URI: https://cronfa.swan.ac.uk/Record/cronfa1530
first_indexed 2013-07-23T11:47:35Z
last_indexed 2018-02-09T04:28:50Z
id cronfa1530
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spelling 2014-03-20T21:06:25.5008765 v2 1530 2011-10-01 Causality and Micro-Causality in Curved Spacetime ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 28a24f55687c82d6f3ee378ead3cf234 Graham Shore Graham Shore true false 2011-10-01 BGPS It has been known for a long time that vacuum polarization in QED leads to a superluminal low-frequency phase velocity for light propagating in curved spacetime. Assuming the validity of the Kramers-Kronig dispersion relation, this would imply a superluminal wavefront velocity and the violation of causality. Here, we calculate for the first time the full frequency dependence of the refractive index using world-line sigma model techniques together with the Penrose plane wave limit of spacetime in the neighbourhood of a null geodesic. We find that the high-frequency limit of the phase velocity (i.e. the wavefront velocity) is always equal to c and causality is assured. However, the Kramers-Kronig dispersion relation is violated due to a non-analyticity of the refractive index in the upper-half complex plane, whose origin may be traced to the generic focusing property of null geodesic congruences and the existence of conjugate points. This puts into question the issue of micro-causality, i.e. the vanishing of commutators of field operators at spacelike separated points, in local quantum field theory in curved spacetime. Journal Article Phys. Lett. B 655 67 74 Elsevier 25 10 2007 2007-10-25 10.1016/j.physletb.2007.08.073 Analyses how causality and micro-causality are realised in quantum field theories in curved spacetime. The frequency dependence of the refractive index for QED in curved spacetime is calculated for the first time, showing how superluminal low-frequency propagation is compatible with causality. COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University 2014-03-20T21:06:25.5008765 2011-10-01T00:00:00.0000000 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Timothy Hollowood 0000-0002-3258-320X 1 Graham Shore 2
title Causality and Micro-Causality in Curved Spacetime
spellingShingle Causality and Micro-Causality in Curved Spacetime
Timothy Hollowood
Graham Shore
title_short Causality and Micro-Causality in Curved Spacetime
title_full Causality and Micro-Causality in Curved Spacetime
title_fullStr Causality and Micro-Causality in Curved Spacetime
title_full_unstemmed Causality and Micro-Causality in Curved Spacetime
title_sort Causality and Micro-Causality in Curved Spacetime
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
28a24f55687c82d6f3ee378ead3cf234
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
28a24f55687c82d6f3ee378ead3cf234_***_Graham Shore
author Timothy Hollowood
Graham Shore
author2 Timothy Hollowood
Graham Shore
format Journal article
container_title Phys. Lett. B
container_volume 655
container_start_page 67
publishDate 2007
institution Swansea University
doi_str_mv 10.1016/j.physletb.2007.08.073
publisher Elsevier
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 0
active_str 0
description It has been known for a long time that vacuum polarization in QED leads to a superluminal low-frequency phase velocity for light propagating in curved spacetime. Assuming the validity of the Kramers-Kronig dispersion relation, this would imply a superluminal wavefront velocity and the violation of causality. Here, we calculate for the first time the full frequency dependence of the refractive index using world-line sigma model techniques together with the Penrose plane wave limit of spacetime in the neighbourhood of a null geodesic. We find that the high-frequency limit of the phase velocity (i.e. the wavefront velocity) is always equal to c and causality is assured. However, the Kramers-Kronig dispersion relation is violated due to a non-analyticity of the refractive index in the upper-half complex plane, whose origin may be traced to the generic focusing property of null geodesic congruences and the existence of conjugate points. This puts into question the issue of micro-causality, i.e. the vanishing of commutators of field operators at spacelike separated points, in local quantum field theory in curved spacetime.
published_date 2007-10-25T18:07:26Z
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score 11.047674

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