Coarse-grained models for loop quantum gravity and their renormalization
Abstract
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.
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BibTeX
@misc{assanioussi2026coarsegrained,
title = {{Coarse-grained models for loop quantum gravity and their renormalization}},
author = {Mehdi Assanioussi and Martin Zeiß},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31152},
eprint = {2608.31152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31152},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Coarse-grained models for loop quantum gravity and their renormalization
AU - Mehdi Assanioussi
AU - Martin Zeiß
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31152
UR - https://arxiv.org/abs/2608.31152
AB - 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.
ER -