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періодичних видань НАН України
періодичних видань НАН України
Modular Theory, Non-Commutative Geometry and Quantum Gravity
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Modular Theory, Non-Commutative Geometry and Quantum Gravity
Інший ID:
2010 Mathematics Subject Classification: 46L87; 46L51; 46L10; 46M15; 18F99; 58B34; 81R60; 81T05; 83C65
doi:10.3842/SIGMA.2010.067
doi:10.3842/SIGMA.2010.067
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
457
Завантажень:
271
Анотація:
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.
