Willkommen zum Oberseminar Mathematische Physik

Causal fermion systems provide a general framework for the formulation of relativistic quantum theory. The aim of the talk is to give a simple introduction and overview, with an emphasis on conceptual issues. In order to motivate the basic objects, we begin with spinors in Minkowski space. Choosing a subspace of the solution space of the Dirac equation and forming the so-called local correlation matrices, one gets simple examples of causal fermion systems. This leads us to the abstract definition of causal fermion systems, where the physical system is described by a measure on a topological space formed of linear operators on a Hilbert space. By specializing, we recover earlier notions like fermion systems in discrete space-time and the fermionic projector. Dynamical equations are formulated by minimizing the so-called causal action. In the second part of the talk, we outline how interacting quantum field theory is described in this framework.

We consider the scattering process of two ions. Let h be roughly the ratio of the electron's mass over the nucleus' mass. For h small, we provide an approximation of the waves operators. The true waves operators are closed to the corresponding waves operators for an effective operator (adiabatic operator). We review also time-dependent and stationary results in this framework.

In this talk I shall (try to) explain the meaning of the words of its title. It is intended for non experts, and aimed to describe a formulation, more than results.