Reduction of quantum systems and the local Gauss law

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and...

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Detalles Bibliográficos
Autores principales: Stienstra, Ruben, van Suijlekom, Walter D.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182777/
https://www.ncbi.nlm.nih.gov/pubmed/30369712
http://dx.doi.org/10.1007/s11005-018-1092-x
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author Stienstra, Ruben
van Suijlekom, Walter D.
author_facet Stienstra, Ruben
van Suijlekom, Walter D.
author_sort Stienstra, Ruben
collection PubMed
description We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796–1808, 2002; J Math Phys 46:032303, 2004).
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spelling pubmed-61827772018-10-24 Reduction of quantum systems and the local Gauss law Stienstra, Ruben van Suijlekom, Walter D. Lett Math Phys Article We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796–1808, 2002; J Math Phys 46:032303, 2004). Springer Netherlands 2018-05-03 2018 /pmc/articles/PMC6182777/ /pubmed/30369712 http://dx.doi.org/10.1007/s11005-018-1092-x Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Stienstra, Ruben
van Suijlekom, Walter D.
Reduction of quantum systems and the local Gauss law
title Reduction of quantum systems and the local Gauss law
title_full Reduction of quantum systems and the local Gauss law
title_fullStr Reduction of quantum systems and the local Gauss law
title_full_unstemmed Reduction of quantum systems and the local Gauss law
title_short Reduction of quantum systems and the local Gauss law
title_sort reduction of quantum systems and the local gauss law
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182777/
https://www.ncbi.nlm.nih.gov/pubmed/30369712
http://dx.doi.org/10.1007/s11005-018-1092-x
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