Crossed products, extended phase spaces and the resolution of entanglement singularities
We identify a direct correspondence between the crossed product construction which plays a crucial role in the theory of Type III von Neumann algebras, and the extended phase space construction which restores the integrability of non-zero charges generated by gauge symmetries in the presence of spat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-02-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321324000191 |
| _version_ | 1797324397870055424 |
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| author | Marc S. Klinger Robert G. Leigh |
| author_facet | Marc S. Klinger Robert G. Leigh |
| author_sort | Marc S. Klinger |
| collection | DOAJ |
| description | We identify a direct correspondence between the crossed product construction which plays a crucial role in the theory of Type III von Neumann algebras, and the extended phase space construction which restores the integrability of non-zero charges generated by gauge symmetries in the presence of spatial substructures. This correspondence provides a blue-print for resolving singularities which are encountered in the computation of entanglement entropy for subregions in quantum field theories. The extended phase space encodes quantities that would be regarded as ‘pure gauge’ from the perspective of the full theory, but are nevertheless necessary for gluing together, in a path integral sense, physics in different subregions. These quantities are required in order to maintain gauge covariance under such gluings. The crossed product provides a consistent method for incorporating these necessary degrees of freedom into the operator algebra associated with a given subregion. In this way, the extended phase space completes the subregion algebra and subsequently allows for the assignment of a meaningful, finite entropy to states therein. |
| first_indexed | 2024-03-08T05:55:35Z |
| format | Article |
| id | doaj.art-5b278f9cf41043f7b90267da98515d00 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-03-08T05:55:35Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-5b278f9cf41043f7b90267da98515d002024-02-05T04:30:58ZengElsevierNuclear Physics B0550-32132024-02-01999116453Crossed products, extended phase spaces and the resolution of entanglement singularitiesMarc S. Klinger0Robert G. Leigh1Corresponding author.; Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois, 1110 West Green St., Urbana, IL 61801, USAIllinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois, 1110 West Green St., Urbana, IL 61801, USAWe identify a direct correspondence between the crossed product construction which plays a crucial role in the theory of Type III von Neumann algebras, and the extended phase space construction which restores the integrability of non-zero charges generated by gauge symmetries in the presence of spatial substructures. This correspondence provides a blue-print for resolving singularities which are encountered in the computation of entanglement entropy for subregions in quantum field theories. The extended phase space encodes quantities that would be regarded as ‘pure gauge’ from the perspective of the full theory, but are nevertheless necessary for gluing together, in a path integral sense, physics in different subregions. These quantities are required in order to maintain gauge covariance under such gluings. The crossed product provides a consistent method for incorporating these necessary degrees of freedom into the operator algebra associated with a given subregion. In this way, the extended phase space completes the subregion algebra and subsequently allows for the assignment of a meaningful, finite entropy to states therein.http://www.sciencedirect.com/science/article/pii/S0550321324000191 |
| spellingShingle | Marc S. Klinger Robert G. Leigh Crossed products, extended phase spaces and the resolution of entanglement singularities Nuclear Physics B |
| title | Crossed products, extended phase spaces and the resolution of entanglement singularities |
| title_full | Crossed products, extended phase spaces and the resolution of entanglement singularities |
| title_fullStr | Crossed products, extended phase spaces and the resolution of entanglement singularities |
| title_full_unstemmed | Crossed products, extended phase spaces and the resolution of entanglement singularities |
| title_short | Crossed products, extended phase spaces and the resolution of entanglement singularities |
| title_sort | crossed products extended phase spaces and the resolution of entanglement singularities |
| url | http://www.sciencedirect.com/science/article/pii/S0550321324000191 |
| work_keys_str_mv | AT marcsklinger crossedproductsextendedphasespacesandtheresolutionofentanglementsingularities AT robertgleigh crossedproductsextendedphasespacesandtheresolutionofentanglementsingularities |