Jena 2013 – wissenschaftliches Programm

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GR: Fachverband Gravitation und Relativitätstheorie

GR 3: Hauptvorträge: Mathematische Methoden

GR 3.1: Hauptvortrag

Dienstag, 26. Februar 2013, 11:15–12:00, HS 6

Causal fermion systems: A quantum space-time emerging from an action principle — •Felix Finster — Mathematics Department, University of Regensburg, Germany

Causal fermion systems provide a general framework for the formulation of relativistic quantum theory. A particular feature is that space-time is a secondary object which emerges by minimizing an action. The aim of the talk is to give a simple introduction, with an emphasis on conceptual issues. We begin with Dirac spinors in Minkowski space and explain how to formulate the system as a causal fermion system. As an example in curved space-time, we then consider spinors on a globally hyperbolic space-time. An example on a space-time lattice illustrates that causal fermion systems also allow for the description of discrete space-times. These examples lead us to the general definition of causal fermion systems. The causal action principle is introduced. We outline how for a given minimizer, one has notions of causality, connection and curvature, which generalize the classical notions and give rise to a proposal for a "quantum geometry". In the last part of the talk, we outline how quantum field theory can be described in this framework and discuss the relation to other approaches.