**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

AMS Member Price: $56.80

MAA Member Price: $63.90

**Electronic ISBN: 978-1-4704-3824-1
Product Code: AMSIP/35.E**

List Price: $71.00

AMS Member Price: $56.80

MAA Member Price: $63.90

#### 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

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.

#### Readership

Graduate students and research mathematicians interested in mathematical physics.

#### Reviews & Endorsements

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

-- Zentralblatt MATH

# Table of Contents

## The Principle of the Fermionic Projector

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- The principle of the Fermionic projector–A new mathematical model of space-time 110
- Preliminaries 716
- The Fermionic projector in the continuum 2938
- The principle of the Fermionic projector 7180
- The continuum limit 8998
- The Euler-Lagrange equations in the vacuum 123132
- The dynamical gauge group 149158
- Spontaneous block formation 167176
- The effective gauge group 189198
- Appendix A. Connection to the Fock space formalism 199208
- Appendix B. Some formulas of the light-cone expansion 203212
- Appendix C. Normalization of chiral fermions 207216
- Appendix D. The regularized causal perturbation theory 233242
- Appendix E. Linear independence of the basic fractions 249258
- Appendix F. The commutator [𝑃,𝑄] 259268
- Appendix G. Perturbation calculation for the spectral decomposition of 𝑃(𝑥,𝑦)𝑃(𝑦,𝑥) 281290
- Bibliography 295304
- Index 297306
- Notation index 301310
- Back Cover Back Cover1314