arXiv subjects

Carlos E. Beltrán

Publications and source records attributed to Carlos E. Beltrán.

3 recordsLinked to original sources

arXiv2026

Causal Structure for Generalized Spinfoams

We investigate the role of causality in the generalized EPRL spinfoam model introduced by Kaminski, Kisielowski, and Lewandowski (EPRL-KKL). We first propose a definition of causal structure on an arbitrary 2-complex and analyze how causal orientations can be assigned to its 1-skeleton and 2-skeleton. We identify a criterion that determines when an orientation of the 2-skeleton induces a consistent causal structure on the 1-skeleton. This characterization naturally involves tools from graph theory and linear algebra over the Galois field $\mathbb{F}_2$. Using these results, we introduce a causal vertex amplitude that generalizes previous proposals by Bianchi--Dussaud and Bianchi--Chen--Gamonal. We study its asymptotic behavior and revisit the interpretation of the two critical points appearing in the semiclassical analysis of the EPRL and EPRL-KKL spinfoam models. Finally, we discuss several directions in which the causal amplitude introduced here may provide new insights for future developments, like the cosine problem and the presence of irregular light cone structures.

gr-qc↗

arXiv2026

FALSE: The EPRL amplitude is supported on flat connections

There is an error in our recent preprint ``The EPRL amplitude is supported on flat connections''. The error is in Section 3. Here we leave the original text unchanged, but add a note in Section 3 pointing out exactly what the error is. We apologize for the false alarm. After one month, this preprint will be withdrawn from the arxiv. {\bf Original Abstract:} For the version of the EPRL model based on the original vertex amplitude and the face amplitude selected by its gluing properties, we prove that the EPRL amplitude of any region with the topology of a 4-ball is supported on flat connections. We state immediate consequences of this result, comment on some applications, and discuss physical implications. The results hold in general; they do not rely on a semiclassical analysis.

gr-qc↗

arXiv2023

A discretization of Holst's action for general relativity

We present a simplicial model for gravity written in terms of a discretized Lorentz connection and a discretized tetrad field. The continuum limit of its action is Holst's action for general relativity. With the intention of using it to construct spin foam modes for quantum gravity, we write two other equivalent models written in terms of a discretized and constrained $B$ field. The differences between our model and existing models are most likely inessential in the sense that a quantization would lead to equivalent quantum theories in the Wilsonian continuum limit. Nevertheless, we mention two features leading to possible advantages: Curvature degrees of freedom are described at the level of each 4-simplex. Our model offers a picture of bulk geometry leading to actions for matter couplings that split as a sum over 4-simplices.

gr-qc↗