Causal variational principles and conservation laws

The theory of causal fermion systems is an approach to describe fundamental physics. It gives quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for desribing and analyzing non-smooth geometries. The dynamics is described by so-called causal variational principles.

The talk focuses on causal variational principles from the perspective of analysis and the calculus of variations. After a simple introduction to causal variational principles, I shall explain how Noether-like theorems can be formulated in this setting. The basic method is to work with so-called surface layer integrals, which I will introduce. The simplest version of a Noether-like theorem is proven. At the end of the talk, I will give an outlook on causal fermion systems and explain how our Noether-like theorems are related to the conservation laws for charge and energy-momentum in relativistic quantum theory.

This is joint work with Johannes Kleiner (Regensburg).