The Continuum Limit of Causal Fermion Systems

TL;DR

This monograph presents the mathematical framework of causal fermion systems, aiming to unify quantum mechanics, general relativity, and quantum field theory through a novel variational principle.

Contribution

It introduces the causal action principle and demonstrates its ability to derive standard model interactions and gravity within a rigorous mathematical setting.

Findings

Causal fermion systems encompass quantum and gravitational physics as limiting cases.

The causal action principle provides a new variational approach to fundamental interactions.

Mathematically connects causal fermion systems with physical theories in Minkowski space.

Abstract

This monograph 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, called the causal action principle. In addition to the basics, the book provides all the necessary mathematical background and explains how the causal action principle gives rise to the interactions of the standard model plus gravity on the level of second-quantized fermionic fields coupled to classical bosonic fields. The focus is on getting a mathematically sound connection between causal fermion systems and physical systems in Minkowski space. The book is intended for graduate students entering the field, and is furthermore a valuable reference work for researchers in quantum field theory and quantum gravity.