Hopf link volume simplicity constraints in spin foam models. (21st September 2020)

• Record Type: Journal Article
• Authors: Assanioussi, Mehdi; Bahr, Benjamin
• Is Part Of: Classical and quantum gravity. Volume 37:Number 20(2020:Oct.)
• Publication Date: 2020-09-21
• Subjects: spin foam models -- quantum gravity -- bivector geometries -- simplicity constraints -- Hopf link volume; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/abb117
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: In this article we consider specific bivector geometries which arise in the large-spin limit of the extension of the Engle–Pereira–Rovelli–Livine spin foam model for quantum gravity by Kaminski, Kisielowski and Lewandowski. We address the implementation of volume simplicity constraints, which are required to ensure that a 4 d metric can be reconstructed from the bivector geometry. We find that the necessary conditions are closely related, but not quite equal to the Hopf link volume simplicity constraints introduced in earlier works. We estimate the number of independent geometricity conditions for arbitrary bivector geometries, and find that they always agree with the number of Hopf links on the graph minus one, suggesting that the geometricity conditions can generically be formulated by deformation of the Hopf link volume simplicity constraints.