AMSIP/35: The principle of the fermionic projector费米投影仪原理
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作者： Felix Finster著
出 版 社：
出版时间： 2006-2-1字数：版次： 1页数： 302印刷时间： 2006/02/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780821839744包装： 平装内容简介
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.
目录
Preface
Chapter 0. The Principle of the Fermionic Projector - A New Mathematica Model of Space-Time
Chapter 1. Preliminaries
1.1. Relativity
1.2. Relativistic Quantum Mechanics
1.3. Fock Space Quantization of the Free Dirac Field
1.4. Classical Gauge Theories
1.5. Dirae Spinors in Curved Space-Time
Chapter 2. The Fermionic Projector in the Continuum
2.1. The External Field Problem
2.2. The Causal Perturbation Expansion
2.3. Definition of the Fermionic Projector
2.4. Interpretation and Consequences
2.5. The Light-Cone Expansion
2.6. Normalization of the Fermionic States
Chapter 3. The Principle of the Fermionic Projector
3.1. Connection between Local Gauge Freedom and the Measurability of Position and Time
3.2. Projection on Fermionic States
3.3. Discretization of Space-Time
3.4. The Principle of the Fermionic Projector
3.5. A Variational Principle
3.6. Discussion
Chapter 4. The Continuum Limit
4.1. The Method of Variable Regularization
4.2. The Regularized Product P(x,y) P(y, x) in the Vacuum
4.3. The Regularized Vacuum on the Light Cone, Scalar Component
4.4. The Regularized Vacuum on the Light Cone, Vector Component
4.5. The General Formalism
Chapter 5. The Euler-Lagrange Equations in the Vacuum
5.1. The Fermion Configuration of the Standard Model
5.2. The General Two-Point Action
5.3. The Spectral Decomposition of P(x, y) P(y,x)
5.4. Strong Spectral Analysis of the Euler-Lagrange Equations
5.5. Motivation of the Lagrangian, the Mass Degeneracy Assumption
5.6. Stability of the Vacuum
Chapter 6. The Dynamical Gauge Group
6.1. The Euler-Lagrange Equations to Highest Degree on the Light Cone
6.2. The Gauge Terms in the Euler-Lagrange Equations
Chapter 7. Spontaneous Block Formation
7.1. The Partial Trace and the Dynamical Mass Matrices
7.2. Analysis of Degeneracies
7.3. The Dynamical Mass Matrices in the Quark and Neutrino Blocks
Chapter 8. The Effective Gauge Group
8.1. The Chiral Transformation in the Quark Blocks
8.2. The Chiral Transformation in the Lepton Block
8.3. Derivation of 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
C.1. Massive Chiral Fermions - Preparatory Discussion
C.2. The Homogeneous Perturbation Expansion
C.3. The General Construction, Proof of Idempotence
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)
G.1. Perturbation of Invariant Subspaces
G.2. Factorization of Matrix Traces
G.3. Calculation of the Matrix Traces
G.4. Perturbation of the Non-Zero Eigenvalues
G.5. Perturbation of the Kernel
Bibliography
Index
Notation Index