Causal spinfoam vertex for 4d Lorentzian quantum gravity

TL;DR

This paper introduces a new causal spinfoam vertex for 4d Lorentzian quantum gravity, incorporating Toller T-matrices and analyzing their properties, leading to insights on causal structures and geometries in quantum gravity.

Contribution

It presents a novel causal spinfoam vertex using Toller T-matrices, connecting to existing models and analyzing causal and geometric properties in the large-spin limit.

Findings

Toller T-matrices encode causal data in the vertex

Cancellation of Toller poles in the EPRL vertex

Selection of Lorentzian Regge geometries with causal data

Abstract

We introduce a new causal spinfoam vertex for $4$d Lorentzian quantum gravity. The causal data are encoded in Toller $T$-matrices, which add to Wigner $D$-matrices $T^{(+)}+T^{(-)}=D$, and for which we provide a Feynman $\mathrm{i}\varepsilon$ representation. We discuss how the Toller poles cancel in the EPRL vertex, how the Livine-Oriti model is obtained in the Barrett-Crane limit, and how spinfoam causal data are distinct from Regge causal data. In the large-spin limit, we show that only Lorentzian Regge geometries with causal data compatible with the spinfoam data are selected, resulting in a single exponential $\exp(+\mathrm{i}\, S_{\mathrm{Regge}}/\hbar)$ and a new form of causal rigidity.