Martin Zeiß | Searcharxiv

arXiv2026

Coarse-grained models for loop quantum gravity and their renormalization

We introduce a family of effective theories and use them to define a specific type of coarse-grained models for canonical loop quantum gravity. Each effective theory is characterized by two parameters and it consists mainly of a Hilbert space of coarse states and an effective Hamiltonian operator. The construction of the coarse Hilbert spaces relies on a systematic coarse-graining procedure for spin network states. The effective Hamiltonians are then obtained from an analysis of the interplay between this coarse-graining procedure and the action of various Hamiltonian operators defined in loop quantum gravity. Finally, we provide a prescription for implementing the Hamiltonian non-perturbative renormalization framework for the coarse-grained models, and we explicitly write down the renormalization flow equations. The aim of this work is to build an arena for studying the emergence of the continuum limit and the derivation of phenomenological models in the context of canonical loop quantum gravity.

hep-th↗

arXiv2025

Bell states for fermions in loop quantum gravity

Fermion fields are fundamental for the description of nature and also fit very naturally into the framework of loop quantum gravity. Motivated partially by proposals to use gravitationally mediated entanglement of matter as a witness for the quantum nature of gravity, we investigate how such entanglement can be defined and investigated in loop quantum gravity. In particular, we ask how a pair of fermions in a Bell state could be described in loop quantum, gravity. We demonstrate that the notion of fermionic entanglement in loop quantum gravity is subtle, by showing that some potential ways to define it fail. We then investigate a kinematical observable involving both, fermionic and gravitational degrees of freedom, the component of the fermion spin normal to a surface. We study its properties, and compare it to the standard operator for components of spin in a given direction in quantum mechanics. Using these normal components of spin, we define a kinematical observable that measures the correlation between space-like separated fermions which closely mirrors the CHSH observable. Finally, we exhibit states of the fermions coupled to quantum geometry that violate the Bell-CHSH inequality.

gr-qc↗