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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this work we study a Spin Foam model for 4d Riemannian gravity, andpropose a new way of imposing the simplicity constraints that uses the recentlydeveloped holomorphic representation. Using the power of the holomorphicintegration techniques, and with the introduction of two new tools: thehomogeneity map and the loop identity, for the first time we give the analyticexpressions for the behaviour of the Spin Foam amplitudes under 4-dimensionalPachner moves. It turns out that this behaviour is controlled by an insertionof nonlocal mixing operators. In the case of the 5-1 move, the expressiongoverning the change of the amplitude can be interpreted as a vertexrenormalisation equation. We find a natural truncation scheme that allows us toget an invariance up to an overall factor for the 4-2 and 5-1 moves, but notfor the 3-3 move. The study of the divergences shows that there is a range ofparameter space for which the 4-2 move is finite while the 5-1 move diverges.This opens up the possibility to recover diffeomorphism invariance in thecontinuum limit of Spin Foam models for 4D Quantum Gravity.

Pachner moves in a 4d Riemannian holomorphic Spin Foam model