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The two body problem in general relativity is of great theoretical and observational interest, and can be studied in the post-Newtonian, post-Minkowskian and small mass ratio approximations, as well as with effective one body and fully numerical techniques. An issue that arises is whether the motion can be decomposed into dissipative and conservative sectors for which the conservative sector admits a Hamiltonian description. This has been established to various orders in the post-Newtonian and post-Minkowskian approximations. In this talk, I will go over recent work where we showed that in the small mass ratio approximation, the motion of a (spinning) point particle under the conservative piece of the first-order self force is Hamiltonian in any stationary spacetime. After this, I describe two issues that arise when attempting to extend these results to subleading order in the mass ratio, namely infrared divergences and ambiguities in the conservative/dissipative splittings. I suggest resolutions of these issues and successfully derive a subleading Hamiltonian conservative sector for the scalar self force, as a toy model for the gravitational case.

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I will review recent progress in the asymptotic safety approach to quantum gravity. This includes the computation of momentum-dependent graviton correlation functions, the structure of the Standard Model with asymptotically safe gravity, and the recent first computation directly in space-times with Lorentzian signatures via the spectral function of the graviton. Overall, I will display the progress towards the computation of the quantum effective action which encapsulates effective field theory in the IR limit and the asymptotic safety regime in the UV limit.

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