**AMS/IP Studies in Advanced Mathematics**

Volume: 35;
2006;
302 pp;
Hardcover

MSC: Primary 83; 81;
**Print ISBN: 978-0-8218-3974-4
Product Code: AMSIP/35**

List Price: $71.00

Individual Member Price: $56.80

#### Supplemental Materials

# The Principle of the Fermionic Projector

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*Felix Finster*

A co-publication of the AMS and International Press of Boston, Inc.

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.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

#### Table of Contents

# Table of Contents

## The Principle of the Fermionic Projector

#### Readership

Graduate students and research mathematicians interested in mathematical physics.

#### Reviews

This book by Felix Finster presents in its 300 pages a good, and partially unusual approach to relativistic quantum field theory.

-- Zentralblatt MATH