2025-04-07 - 2025-04-11
Renate Loll
Radboud University Nijmegen
Quantum gravity, the elusive quantum theory underlying general relativity, is _the_ missing piece in our understanding of the fundamental interactions. Because of the extreme smallness of its characteristic distance scale, the Planck length, constructing a theory that makes new, testable predictions would be an amazing feat in terms of pushing conceptual and computational boundaries. However, there is still no consensus on the structure and aims of quantum gravity, and it can be difficult for beginners and outsiders to understand what is going on in the field.
Keeping this in mind, the lectures will provide a larger context, address conceptual and structural issues, which distinguish quantum gravity from quantum gauge field theories, and explain the different starting points of past and present approaches. In addition, they will describe a concrete pathway for quantum gravity in a post-string and -loop era, given by modern lattice quantum gravity based on causal dynamical triangulations (CDT). The power and successes of this purely quantum field theoretic and nonperturbative formulation derive from a technical set-up that incorporates the principles of both general relativity and quantum theory from the outset, and does not rely on any “exotic” ingredients.
Among the topics covered will be the perturbative and nonperturbative gravitational path integrals, together with diffeomorphism invariance, analytic continuation ("Wick rotation"), conformal divergence, unitarity and computability. We will also look at geometric concepts beyond those of smooth, classical metric spaces, including Regge calculus, random geometry and quantum curvature. They are essential for constructing observables, whose spectral properties can be measured numerically in CDT quantum gravity and have already given us first, quantitative insights into the properties of quantum spacetime in a Planckian regime.
