1:30 pm MCP 201
Does the gravitational path integral define a consistent Hilbert space of quantum-gravitational states? In this talk we formulate general positivity conditions that the path integral must satisfy for overlaps between states—prepared by Euclidean manifolds with specified boundaries—to behave as genuine inner products, ensuring nonnegative norms and a probabilistic interpretation for both open- and closed-universe sectors. While these constraints look highly restrictive, we show that they are nevertheless satisfied in a range of nontrivial examples, including settings with wormhole contributions. This yields a well-defined Hilbert-space framework in which one can meaningfully discuss amplitudes and transition probabilities between quantum-gravity states, and it provides a sharp diagnostic of when semiclassical approximations can or cannot define consistent states.