Minicourse on perturbative and nonperturbative treatment of quantum gravity problems

Advanced subjects and complicated applications. Applications to the interacting theories. Appelquist and Carazzone theorem in QED. Decupling of massive degrees of freedom in polynomial higher derivative quantum gravity: mixed diagrams. Non-local theories of quantum gravity. On the possibility of the universal IR limit in quantum gravity

Basic calculations and basic results. One-loop Feynman diagrams and derivation of the nonlocal form factors for the two-point function. High-energy and low-energy limits. Quadratic decoupling in the IR. Curved-space calculation using the heat-kernel solution. Applications to the fourth-derivative terms in the one-loop effective action of gravity

Beyond Einstein’s theory. Higher derivative theories of Gravity. Singularities and black holes. Models of Inflation. Consistency checks. Kallen-Lehmann representation. Horava-Lifshitz theories. Infrared problems. Other approaches.

In this talk I will describe recent proposed experimental setups developed to test the quantum nature of gravity and how they can be used to test different quantum theories. After a brief overview of the motivations behind those setups, I will show how, in the context of canonical quantum gravity, one can derive quantum gravitational corrections for an approximate Schrödinger equation for matter fields in a fixed background. The corrections can be non-linear and non-Hermitian, which poses a series of problems. I will focus on the non-Hermitian terms, their interpretation and their possible observational consequences in different scenarios. I will then describe the differences in the pilot-wave approach to quantum gravity, how it offers a natural interpretation for the corrections in terms of the Quantum Equilibrium Hypothesis and a path for deriving the effects of such corrections in tabletop experiments. If there is time, I will comment on the nonlinear modifications of the Schrödinger equations, on a recent attempt to introduce them in the path integral formalism of EFT quantum gravity in a consistent manner (Correlated Worldline Theory) and on their phenomenological consequences.

Covariant Formalism. Perturbation theory. Gauge fixing. Becchi Rouet Stora Tyutin symmetry and diffeomorphism invariance. One loop and two loop ultraviolet divergencies. Renormalization problems. Euclidean gravity. Gravitational instantons.

Introduction to Quantum Gravity. Canonical formalism of Einstein gravity. DeWitt metric. Arnowit-Deser-Misner constraints analysis. Physical interpretation of constrains. Quantization. Wheeler-DeWitt equation. Wave function of the Universe. Minisuperspace. Conceptual issues.