Willkommen zum Oberseminar Mathematische Physik

We consider the quantum mechanical time evolution of a many particle fermionic system which interacts with a so called tracer particle. We focus on the question whether it is possible to describe the tracer particle by some free, one particle evolution equation, which arises in our model from the replacement of the full Hamiltonian by the conjectured mean field Hamiltonian. Using perturbation theory, we will investigate this problem on a mathematical rigorous level. It is shown that the quantum density fluctuations are partially responsible for the deviation from free evolution. In dimension one, the fluctuations of the emergent potential are shown to be constant. This will be used to prove convergence of the real time evolution to its mean field dynamics. In contrast to prior results about mean field dynamics, the Hamiltonian considered in the theorem does not require the scaling of the potential.

I will start with a short story, hopefully entertaining. Then I will discuss the general philosophy of precision computations of Lamb shifts using QED, based in particular on the works of Shabaev and Pachucki. I will explain two kinds of effective Hamiltonians. Then I will discuss the formalism of time-ordered and 2-times Green's functions. Finally, if there is still time, I will talk about the structure of QED and possible perturbative approaches, which are relevant for bound state computations.