Holonomy Observables for the Turaev–Viro Model of Quantum Gravity

ABSTRACT This paper presents a proposal for the study of holonomy observables for the Turaev–Viro model, a model of three‐dimensional Loop Quantum Gravity with a positive cosmological constant. A review of central aspects of Loop Quantum Gravity and of a categorical formalism for discrete gauge theories is presented with the intent to contextualize the Turaev–Viro model within a more general setting, which clarifies the role of the Hopf algebra in its construction. The key results on spin observables for the Turaev–Viro model and on holonomy observables for the Ponzano–Regge model are presented as an effort to develop a theory of holonomy observables for the Turaev–Viro model.