Modular Theory, Non-Commutative Geometry and Quantum Gravity
This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2010 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146505 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modular Theory, Non-Commutative Geometry and Quantum Gravity / P. Bertozzini, R. Conti, W. Lewkeeratiyutkul // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 260 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862688395023613952 |
|---|---|
| author | Bertozzini, P. Conti, R. Lewkeeratiyutkul, W, |
| author_facet | Bertozzini, P. Conti, R. Lewkeeratiyutkul, W, |
| citation_txt | Modular Theory, Non-Commutative Geometry and Quantum Gravity / P. Bertozzini, R. Conti, W. Lewkeeratiyutkul // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 260 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
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| first_indexed | 2025-12-07T16:08:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146505 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:08:30Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bertozzini, P. Conti, R. Lewkeeratiyutkul, W, 2019-02-09T19:32:28Z 2019-02-09T19:32:28Z 2010 Modular Theory, Non-Commutative Geometry and Quantum Gravity / P. Bertozzini, R. Conti, W. Lewkeeratiyutkul // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 260 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L87; 46L51; 46L10; 46M15; 18F99; 58B34; 81R60; 81T05; 83C65 doi:10.3842/SIGMA.2010.067 https://nasplib.isofts.kiev.ua/handle/123456789/146505 This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal. This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
 P.B. wishes to thank C. Rovelli at CPT in Marseille, J. Barrett at the QG2
 -2008 conference at the university of Nottingham and S.J. Summers at the university of Florida in Gainesville, for the opportunities to discuss some of the ideas and of fer seminars exposing most of the original material here presented, in May, July 2008 and in April 2009.
 We thank one of the anonymous referees of the paper for pointing out some missing referenceson modular localization and on the algebraic proof of Bisognano–Wichmann theorem based onscattering theory in Section 3. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Modular Theory, Non-Commutative Geometry and Quantum Gravity Article published earlier |
| spellingShingle | Modular Theory, Non-Commutative Geometry and Quantum Gravity Bertozzini, P. Conti, R. Lewkeeratiyutkul, W, |
| title | Modular Theory, Non-Commutative Geometry and Quantum Gravity |
| title_full | Modular Theory, Non-Commutative Geometry and Quantum Gravity |
| title_fullStr | Modular Theory, Non-Commutative Geometry and Quantum Gravity |
| title_full_unstemmed | Modular Theory, Non-Commutative Geometry and Quantum Gravity |
| title_short | Modular Theory, Non-Commutative Geometry and Quantum Gravity |
| title_sort | modular theory, non-commutative geometry and quantum gravity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146505 |
| work_keys_str_mv | AT bertozzinip modulartheorynoncommutativegeometryandquantumgravity AT contir modulartheorynoncommutativegeometryandquantumgravity AT lewkeeratiyutkulw modulartheorynoncommutativegeometryandquantumgravity |