Non-convex 4d polytopes in Spin Foam Models

Abstract

In this article we consider non-convex $4d$ polytopes in ${\mathbb{R}}^4$. The paper consist of two parts: Firstly, we extend the proof of the formula for the $4d$ volume in terms of $2d$ face bivectors and boundary graph crossings from convex to non-convex polytopes. Secondly, we consider the EPRL-FK spin foam model, and demonstrate that there exists boundary data which leads to non-convex $4d$ polytopes in the asymptotic analysis of the vertex amplitude.

25 pages, 17 figures (14 images, 3 tables)

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Cited by in corpus (2)

• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors