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The Principle of the Fermionic Projector
 
Felix Finster Universität Regensburg, Regensburg, Germany
A co-publication of the AMS and International Press of Boston
Front Cover for The Principle of the Fermionic Projector
Available Formats:
Hardcover ISBN: 978-0-8218-3974-4
Product Code: AMSIP/35
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $60.80
Electronic ISBN: 978-1-4704-3824-1
Product Code: AMSIP/35.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $56.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $114.00
MAA Member Price: $102.60
AMS Member Price: $91.20
Front Cover for The Principle of the Fermionic Projector
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  • Front Cover for The Principle of the Fermionic Projector
  • Back Cover for The Principle of the Fermionic Projector
The Principle of the Fermionic Projector
Felix Finster Universität Regensburg, Regensburg, Germany
A co-publication of the AMS and International Press of Boston
Available Formats:
Hardcover ISBN:  978-0-8218-3974-4
Product Code:  AMSIP/35
List Price: $76.00
MAA Member Price: $68.40
AMS Member Price: $60.80
Electronic ISBN:  978-1-4704-3824-1
Product Code:  AMSIP/35.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $56.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $114.00
MAA Member Price: $102.60
AMS Member Price: $91.20
  • Book Details
     
     
    AMS/IP Studies in Advanced Mathematics
    Volume: 352006; 302 pp
    MSC: 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 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.

    Readership

    Graduate students and research mathematicians interested in mathematical physics.

  • Table of Contents
     
     
    • Chapters
    • 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
    • Appendix A. Connection to the Fock space formalism
    • Appendix B. Some formulas of the light-cone 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 $P(x,y) P(y,x)$
  • Reviews
     
     
    • This book by Felix Finster presents in its 300 pages a good, and partially unusual approach to relativistic quantum field theory.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for reviewers who would like to review an AMS book
    Accessibility – to request an alternate format of an AMS title
Volume: 352006; 302 pp
MSC: 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 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.

Readership

Graduate students and research mathematicians interested in mathematical physics.

  • Chapters
  • 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
  • Appendix A. Connection to the Fock space formalism
  • Appendix B. Some formulas of the light-cone 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.