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: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2017
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| 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| _version_ | 1862553473009057792 |
|---|---|
| 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. |
| collection | DSpace DC |
| 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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| first_indexed | 2025-11-25T21:08:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148635 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T21:08:28Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT hagaj factororderingandpathintegralmeasureforquantumgravityin11dimensions AT maitrarl factororderingandpathintegralmeasureforquantumgravityin11dimensions |