Causal spinfoam vertex for 4d Lorentzian quantum gravity

Eugenio Bianchi; Chaosong Chen; Mauricio Gamonal

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arXiv · 2601.23162

Causal spinfoam vertex for 4d Lorentzian quantum gravity

Eugenio Bianchi·Chaosong Chen·Mauricio Gamonal

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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.

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gr-qc hep-th math-ph math.MP

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BibTeX RIS

Eugenio Bianchi, Chaosong Chen, Mauricio Gamonal. 2026-01-30. Causal spinfoam vertex for 4d Lorentzian quantum gravity. https://arxiv.org/abs/2601.23162

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