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Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
Інший ID:
2010 Mathematics Subject Classification: 83C45; 57R56; 83C27
DOI: http://dx.doi.org/10.3842/SIGMA.2012.009
DOI: http://dx.doi.org/10.3842/SIGMA.2012.009
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
596
Завантажень:
272
Анотація:
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.
