Hardcover ISBN:  9780821839744 
Product Code:  AMSIP/35 
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Electronic ISBN:  9781470438241 
Product Code:  AMSIP/35.E 
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Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 35; 2006; 302 ppMSC: Primary 83; 81;
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 spacetime. The mathematical tools are developed for the analysis of the corresponding EulerLagrange 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.ReadershipGraduate students and research mathematicians interested in mathematical physics.

Table of Contents

Chapters

The principle of the Fermionic projector–A new mathematical model of spacetime

Preliminaries

The Fermionic projector in the continuum

The principle of the Fermionic projector

The continuum limit

The EulerLagrange equations in the vacuum

The dynamical gauge group

Spontaneous block formation

The effective gauge group

Appendix A. Connection to the Fock space formalism

Appendix B. Some formulas of the lightcone expansion

Appendix C. Normalization of chiral fermions

Appendix D. The regularized causal perturbation theory

Appendix E. Linear independence of the basic fractions

Appendix F. The commutator $[P,Q]$

Appendix G. Perturbation calculation for the spectral decomposition of $P(x,y) P(y,x)$


Additional Material

Reviews

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


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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 spacetime. The mathematical tools are developed for the analysis of the corresponding EulerLagrange 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.
Graduate students and research mathematicians interested in mathematical physics.

Chapters

The principle of the Fermionic projector–A new mathematical model of spacetime

Preliminaries

The Fermionic projector in the continuum

The principle of the Fermionic projector

The continuum limit

The EulerLagrange equations in the vacuum

The dynamical gauge group

Spontaneous block formation

The effective gauge group

Appendix A. Connection to the Fock space formalism

Appendix B. Some formulas of the lightcone expansion

Appendix C. Normalization of chiral fermions

Appendix D. The regularized causal perturbation theory

Appendix E. Linear independence of the basic fractions

Appendix F. The commutator $[P,Q]$

Appendix G. Perturbation calculation for the spectral decomposition of $P(x,y) P(y,x)$

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