English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We identify a direct correspondence between the crossed product constructionwhich plays a crucial role in the theory of Type III von Neumann algebras, andthe extended phase space construction which restores the integrability ofnon-zero charges generated by gauge symmetries in the presence of spatialsubstructures. This correspondence provides a blue-print for resolvingsingularities which are encountered in the computation of entanglement entropyfor subregions in quantum field theories. The extended phase space encodesquantities that would be regarded as `pure gauge' from the perspective of thefull theory, but are nevertheless necessary for gluing together, in a pathintegral sense, physics in different subregions. These quantities are requiredin order to maintain gauge covariance under such gluings. The crossed productprovides a consistent method for incorporating these necessary degrees offreedom into the operator algebra associated with a given subregion. In thisway, the extended phase space completes the subregion algebra and subsequentlyallows for the assignment of a meaningful, finite entropy to states therein.

Crossed Products, Extended Phase Spaces and the Resolution of Entanglement Singularities