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

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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Main Authors: Haga, J., Maitra, R.L.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148635
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spelling irk-123456789-1486352019-02-19T01:31:27Z Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions Haga, J. Maitra, R.L. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148635 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Haga, J.
Maitra, R.L.
spellingShingle Haga, J.
Maitra, R.L.
Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Haga, J.
Maitra, R.L.
author_sort Haga, J.
title 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_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_sort factor ordering and path integral measure for quantum gravity in (1+1) dimensions
publisher Інститут математики НАН України
publishDate 2017
url http://dspace.nbuv.gov.ua/handle/123456789/148635
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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT hagaj factororderingandpathintegralmeasureforquantumgravityin11dimensions
AT maitrarl factororderingandpathintegralmeasureforquantumgravityin11dimensions
first_indexed 2023-05-20T17:30:55Z
last_indexed 2023-05-20T17:30:55Z
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