Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy mode...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148376 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity / V. Bonzom, A. Laddha // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 119 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862548176537387008 |
|---|---|
| author | Bonzom, V. Laddha, A. |
| author_facet | Bonzom, V. Laddha, A. |
| citation_txt | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity / V. Bonzom, A. Laddha // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 119 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity.
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| first_indexed | 2025-11-25T18:54:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148376 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T18:54:43Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bonzom, V. Laddha, A. 2019-02-18T11:10:19Z 2019-02-18T11:10:19Z 2012 Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity / V. Bonzom, A. Laddha // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 119 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 83C45; 57R56; 83C27 DOI: http://dx.doi.org/10.3842/SIGMA.2012.009 https://nasplib.isofts.kiev.ua/handle/123456789/148376 We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity. This paper is a contribution to the Special Issue \Loop Quantum Gravity and Cosmology". The full collection
 is available at http://www.emis.de/journals/SIGMA/LQGC.html. 
 Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. A.L. is grateful to the Penn-State gravity group, especially Abhay Ashtekar, Miguel Campiglia, Adam Handerson and Casey Tomlin for many discussions related to the dynamical issues in LQG over past year. He is indebted to Madhavan Varadarajan for countably infinite discussions on the Hamiltonian constraint in LQG which crystallized his understanding about many of the issues discussed in this review. Work of A.L. is supported by the NSF grant, PHY-0854743. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity Article published earlier |
| spellingShingle | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity Bonzom, V. Laddha, A. |
| title | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity |
| title_full | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity |
| title_fullStr | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity |
| title_full_unstemmed | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity |
| title_short | Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity |
| title_sort | lessons from toy-models for the dynamics of loop quantum gravity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148376 |
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