Quantizing quantum Ricci curvature

Understand

Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure.

• Besides coordinate invariance, its key features are scalability, computability and robustness.
• We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations.
• Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.