The 'principle of the fermionic projector' provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionic projector, a global object in space-time that generalizes the notion of the Dirac sea.At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible to formulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective interaction which shows many similarities to the interactions of the standard model. The main chapters of the book are easily accessible for beginning graduate students in mathematics or physics. Several appendices provide supplementary material, which will be useful to the experienced researcher.
The principle of the Fermionic projector-A new mathematical model of space-time Preliminaries The Fermionic projector in the continuum The principle of the Fermionic projector The continuum limit The Euler-Lagrange equations in the vacuum The dynamical gauge group Spontaneous block formation The effective gauge group Connection to the Fock space formalism Some formulas of the light-cone expansion Normalization of chiral fermions The regularized causal perturbation theory Linear independence of the basic fractions The commutator $[P,Q]$ Perturbation calculation for the spectral decomposition of $P(x,y) P(y,x)$ Bibliography Index Notation index.