The Theory of Causal Fermion Systems

Overview of the Theory

Our current understanding of the Universe is based on two physical theories. On the one hand, there is Quantum Field Theory which is the appropriate theoretical framework to describe the quantum-mechanical behavior and the mutual interactions of the currently known elementary particles. On the other hand, there is General Relativity which explains the large-scale geometric structure of spacetime and its interaction with the matter and energy content of the Universe. In a nutshell, Quantum Field Theory rules processes on microscopic scales while processes on macroscopic scales are governed by General Relativity. Although the theoretical predictions of both theories have been tested experimentally and confirmed to high precision for countless times, there is still a mystery: How can it be that both theories are extremely successful in describing aspects of the Universe within their respective domains of applicability, but with completely different – and even worse – conceptually incompatible mathematical structures? That this question is not only of purely academic interest but is related to more profound questions about our understanding of the structures, principles and mechanisms of our Universe becomes prominently apparent in our ignorance about the nature of black holes: In order to describe them properly, we have to take into account concepts of both Quantum Field Theory and General Relativity.
In order to overcome this inconsistency and thereby to allow for a deeper understanding, the Theory of Causal Fermion Systems has been developed: It has the potential to give answers as it provides a mathematically consistent theory from which Quantum Field Theory and General Relativity can be reproduced as limiting cases.

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Mathematical Introduction

Physical Introduction