The Continuum Limit of Causal Fermion Systems

Felix Finster

Published 2016-05-16Version 1

The theory of causal fermion systems is a recent approach to 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 describing and analyzing non-smooth geometries and "quantum geometries." The dynamics is described by a novel variational principle, called the causal action principle. This monograph introduces the basic concepts, gives 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 beginning graduate students interested in the topic. Moreover, it is a valuable reference work for researchers in quantum field theory and quantum gravity.