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Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
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, 2017, том 13
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13, випуск за цей рік
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Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
Інший ID:
2010 Mathematics Subject Classification: 81V17; 81S40; 83C80
DOI:10.3842/SIGMA.2017.039
DOI:10.3842/SIGMA.2017.039
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
557
Завантажень:
261
Анотація:
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.
