22 - Effective field theory from gravity and black holes

Summary

We first review general concepts of quantum field theory, like Feynman diagrams and path integrals. Then we define the worldline formalism for quantum field theory, and apply it to gravity, in the case of classical gravity with sources. We describe first an electromagnetic analogy of how to write down the worldline action and obtain physics from it, and then use it in the gravity case, for a black hole or neutron star. We then consider tidal forces in the nonrelativistic regime and find how to describe Love numbers and radiated power, for instance. As a simple example, we consider scalar gravity interacting with a source current and how to obtain information from Feynman diagrams. Then, define Non-Relativistic General Relativity (NRGR), a formalism for the gravitational inspiral of two bodies (e.g., two black holes) and show how to calculate the two-body (or many-body) action from Feynman diagrams and how to obtain the radiated power via gravitational waves. We find the Einstein–Infeld–Hofman Lagrangian for many bodies in the NRGR case.