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Superluminality and UV completion

G. M Shore, Graham Shore

Nuclear Physics B, Volume: 778, Issue: 3, Pages: 219 - 258

Swansea University Author: Graham Shore

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DOI (Published version): 10.1016/j.nuclphysb.2007.03.034

Abstract

The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation...

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Published in: Nuclear Physics B
Published: Elsevier 2007
URI: https://cronfa.swan.ac.uk/Record/cronfa1532
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fullrecord <?xml version="1.0"?><rfc1807><datestamp>2014-03-20T21:09:20.4916295</datestamp><bib-version>v2</bib-version><id>1532</id><entry>2011-10-01</entry><title>Superluminality and UV completion</title><swanseaauthors><author><sid>28a24f55687c82d6f3ee378ead3cf234</sid><firstname>Graham</firstname><surname>Shore</surname><name>Graham Shore</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2011-10-01</date><deptcode>FGSEN</deptcode><abstract>The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation of these constraints implies superluminal propagation, in the sense that the low-frequency limit of the phase velocity vph(0) exceeds c. It is explained why causality is related not to vph(0) but to the high-frequency limit vph(&#x221E;) and how these are related by the Kramers-Kronig dispersion relation, depending on the sign of the imaginary part of the refractive index Im n(&#x3C9;) which is normally assumed positive. Superluminal propagation and its relation to UV completion is investigated in detail in three theories: QED in a background electromagnetic field, where the full dispersion relation for n(&#x3C9;) is evaluated numerically for the first time and the role of the null energy condition T&#x3BC;&#x3BD;k&#x3BC;k&#x3BD; &#x2265; 0 is highlighted; QED in a background gravitational field, where examples of superluminal low-frequency phase velocities arise in violation of the positivity constraints; and light propagation in coupled laser-atom &#x39B;-systems exhibiting Raman gain lines with Im n(&#x3C9;) &amp;#60; 0. The possibility that a negative Im n(&#x3C9;) must occur in quantum field theories involving gravity to avoid causality violation, and the implications for the relation of IR effective field theories to their UV completion, are carefully analysed.</abstract><type>Journal Article</type><journal>Nuclear Physics B</journal><volume>778</volume><journalNumber>3</journalNumber><paginationStart>219</paginationStart><paginationEnd>258</paginationEnd><publisher>Elsevier</publisher><issnPrint/><issnElectronic/><keywords/><publishedDay>3</publishedDay><publishedMonth>9</publishedMonth><publishedYear>2007</publishedYear><publishedDate>2007-09-03</publishedDate><doi>10.1016/j.nuclphysb.2007.03.034</doi><url/><notes>This paper demonstrates that the relation between low-energy effective field theories and their UV completion is more subtle than previously believed and shows that in theories involving gravity at least one apparently fundamental tenet of QFT and S-matrix theory must be violated.</notes><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2014-03-20T21:09:20.4916295</lastEdited><Created>2011-10-01T00:00:00.0000000</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Biosciences, Geography and Physics - Physics</level></path><authors><author><firstname>G. M</firstname><surname>Shore</surname><order>1</order></author><author><firstname>Graham</firstname><surname>Shore</surname><order>2</order></author></authors><documents/><OutputDurs/></rfc1807>
spelling 2014-03-20T21:09:20.4916295 v2 1532 2011-10-01 Superluminality and UV completion 28a24f55687c82d6f3ee378ead3cf234 Graham Shore Graham Shore true false 2011-10-01 FGSEN The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation of these constraints implies superluminal propagation, in the sense that the low-frequency limit of the phase velocity vph(0) exceeds c. It is explained why causality is related not to vph(0) but to the high-frequency limit vph(∞) and how these are related by the Kramers-Kronig dispersion relation, depending on the sign of the imaginary part of the refractive index Im n(ω) which is normally assumed positive. Superluminal propagation and its relation to UV completion is investigated in detail in three theories: QED in a background electromagnetic field, where the full dispersion relation for n(ω) is evaluated numerically for the first time and the role of the null energy condition Tμνkμkν ≥ 0 is highlighted; QED in a background gravitational field, where examples of superluminal low-frequency phase velocities arise in violation of the positivity constraints; and light propagation in coupled laser-atom Λ-systems exhibiting Raman gain lines with Im n(ω) &#60; 0. The possibility that a negative Im n(ω) must occur in quantum field theories involving gravity to avoid causality violation, and the implications for the relation of IR effective field theories to their UV completion, are carefully analysed. Journal Article Nuclear Physics B 778 3 219 258 Elsevier 3 9 2007 2007-09-03 10.1016/j.nuclphysb.2007.03.034 This paper demonstrates that the relation between low-energy effective field theories and their UV completion is more subtle than previously believed and shows that in theories involving gravity at least one apparently fundamental tenet of QFT and S-matrix theory must be violated. COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2014-03-20T21:09:20.4916295 2011-10-01T00:00:00.0000000 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics G. M Shore 1 Graham Shore 2
title Superluminality and UV completion
spellingShingle Superluminality and UV completion
Graham Shore
title_short Superluminality and UV completion
title_full Superluminality and UV completion
title_fullStr Superluminality and UV completion
title_full_unstemmed Superluminality and UV completion
title_sort Superluminality and UV completion
author_id_str_mv 28a24f55687c82d6f3ee378ead3cf234
author_id_fullname_str_mv 28a24f55687c82d6f3ee378ead3cf234_***_Graham Shore
author Graham Shore
author2 G. M Shore
Graham Shore
format Journal article
container_title Nuclear Physics B
container_volume 778
container_issue 3
container_start_page 219
publishDate 2007
institution Swansea University
doi_str_mv 10.1016/j.nuclphysb.2007.03.034
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 The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation of these constraints implies superluminal propagation, in the sense that the low-frequency limit of the phase velocity vph(0) exceeds c. It is explained why causality is related not to vph(0) but to the high-frequency limit vph(∞) and how these are related by the Kramers-Kronig dispersion relation, depending on the sign of the imaginary part of the refractive index Im n(ω) which is normally assumed positive. Superluminal propagation and its relation to UV completion is investigated in detail in three theories: QED in a background electromagnetic field, where the full dispersion relation for n(ω) is evaluated numerically for the first time and the role of the null energy condition Tμνkμkν ≥ 0 is highlighted; QED in a background gravitational field, where examples of superluminal low-frequency phase velocities arise in violation of the positivity constraints; and light propagation in coupled laser-atom Λ-systems exhibiting Raman gain lines with Im n(ω) &#60; 0. The possibility that a negative Im n(ω) must occur in quantum field theories involving gravity to avoid causality violation, and the implications for the relation of IR effective field theories to their UV completion, are carefully analysed.
published_date 2007-09-03T03:04:11Z
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score 11.035655

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