Constructing smooth‑spacetime states in spin‑foam quantum gravity

Construct physical quantum states in four‑dimensional spin‑foam models that approximate smooth spacetimes and demonstrate their emergence, e.g., via phase structure and continuum limits.

Background

Spin‑foam models provide a Lorentzian path‑integral description with a rigorous notion of quantum geometry. A major challenge is to identify physical states that approximate smooth manifold spacetimes.

The text emphasizes the need to connect the rich phase structure seen in simplified models to four‑dimensional spin‑foam amplitudes to realize continuum physics.