Crossed Products, Extended Phase Spaces and the Resolution of Entanglement Singularities
| Autor: | Klinger, Marc S., Leigh, Robert G. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 39 pages, 1 figure, new content added in section 2, clarifications made in section 4. V3: New discussion of generalized entropy in Section 2, citations added. V4: Added Appendix E introducing left Haar systems for Lie groupoids and crossed products of C* algebras by locally compact topological groupoids |
| Databáze: | arXiv |
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