Causal Fermion Systems: An Introduction to Fundamental Structures, Methods and Applications

TL;DR

This textbook introduces causal fermion systems as a promising framework unifying quantum mechanics, general relativity, and quantum field theory, emphasizing their mathematical structures and physical applications.

Contribution

It provides a comprehensive introduction to the theory, including mathematical foundations, physical concepts, and detailed examples, serving as a reference for researchers and students.

Findings

Causal fermion systems unify fundamental physics theories.

The causal action principle governs the dynamics.

Applications include analysis of non-smooth and quantum geometries.

Abstract

This textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields 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 describing and analyzing non-smooth geometries and "quantum geometries." The dynamics is described by a novel variational principle, the causal action principle. The book includes a detailed summary of the mathematical and physical preliminaries. It explains the physical concepts behind the causal fermion system approach from the basics. Moreover, all the mathematical objects and structures are introduced step by step. The mathematical methods used for the analysis of causal fermion systems and the causal action principle are introduced in depth. Many examples and applications are worked out. The textbook is addressed to master and graduate students in mathematics or physics. Furthermore, it serves as a reference work for researchers working in the field.