On the geometry of loop quantum gravity on a graph
Carlo Rovelli, Simone Speziale
TL;DR
This paper explores the geometric structures in loop quantum gravity on graphs, linking twisted geometries to Regge geometries to deepen understanding of quantum spacetime discretizations.
Contribution
It establishes a simple relation between twisted geometries and Regge geometries within the context of loop quantum gravity.
Findings
Derived a relation connecting twisted and Regge geometries.
Clarified the geometric interpretation of quantum states on graphs.
Enhanced understanding of quantum geometric structures in LQG.
Abstract
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
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