Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions

We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the time-evolution operator, one requires that the corresponding Hamiltonian...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2017
Автори: Haga, J., Maitra, R.L.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2017
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/148635
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions / J. Haga, R.L. Maitra // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 35 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Haga, J.
Maitra, R.L.
author_facet Haga, J.
Maitra, R.L.
citation_txt Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions / J. Haga, R.L. Maitra // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 35 назв. — англ.
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container_title Symmetry, Integrability and Geometry: Methods and Applications
description We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the time-evolution operator, one requires that the corresponding Hamiltonian is self-adjoint; this issue is subtle for a particular category of factor orderings. We identify and parametrize a complete set of self-adjoint extensions and provide a canonical description of these extensions in terms of boundary conditions. Moreover, we use Trotter-type product formulae to construct path-integral representations of time evolution.
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language English
last_indexed 2025-11-25T21:08:28Z
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spelling Haga, J.
Maitra, R.L.
2019-02-18T16:48:55Z
2019-02-18T16:48:55Z
2017
Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions / J. Haga, R.L. Maitra // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 35 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81V17; 81S40; 83C80
DOI:10.3842/SIGMA.2017.039
https://nasplib.isofts.kiev.ua/handle/123456789/148635
We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the time-evolution operator, one requires that the corresponding Hamiltonian is self-adjoint; this issue is subtle for a particular category of factor orderings. We identify and parametrize a complete set of self-adjoint extensions and provide a canonical description of these extensions in terms of boundary conditions. Moreover, we use Trotter-type product formulae to construct path-integral representations of time evolution.
The authors are grateful to Renate Loll for many fruitful conversations which informed this
 project, to Jan Ambjørn for the reference to Nakayama’s work on 2D quantum gravity, and to Vincent Moncrief, Antonella Marini, and Maria Gordina for ongoing useful discussions about
 quantization and mathematical physics. Additionally, the authors would like to thank the editor
 and the anonymous reviewers for their thoughtful and insightful comments and suggestions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
Article
published earlier
spellingShingle Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
Haga, J.
Maitra, R.L.
title Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
title_full Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
title_fullStr Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
title_full_unstemmed Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
title_short Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
title_sort factor ordering and path integral measure for quantum gravity in (1+1) dimensions
url https://nasplib.isofts.kiev.ua/handle/123456789/148635
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