Introduction to Algebraic and Constructive Quantum Field Theory

Cover
Princeton Series in Physics
Introduction to Algebraic and Constructive Quantum Field Theory
Copyright
     © 1992 by Princeton University Press
     ISBN 0-691-08546-3
     QC174.45.B29 1991 530.! \'43—dc2O
     LCCN 91-16504

Contents
Preface
Introduction
     The logical structure of quantum field theory
     Organization of the book

1  The Free Boson Field
     1.1. Introduction
     1.2. Weyl and Heisenberg systems
          Problems
     1.3. Functional integration
          Problems
     1.4. QuasI-invariant distributions
          Problems
     1.5 Absolute continuity
          Problems
     1.6. IrreducIbIlity and ergodicity
     1.7. The Fourier-Wiener transform
          Problems
     1.8. The structure or F and wave-particle duality
          Problems
     1.9. Implications of wave-particle duality
     1.10. Characterization of the free boson field
     1.11. The complex wave representation
          Problems
     1.12. Analytic features of the complex wave representation
     Bibliographical Notes on Chapter 1

2  The Free Fermion Field
     2.1. Clifford systems
     2.2. Existence of the free fermion field
     2.3. The real wave representation
     2.4. The complex wave representation
          Problems
     Bibliographical Notes on Chapter 2

3  Properties of the Free Fields
     3.1. Introduction
     3.2. The exponential laws
     3.3. Irreducibility
     3.4. Representation of the orthogonal group by measure-preserving transformations
     3.5. Bosonlc quantizatlon of symplectic dynamics
     3.6. Fermionic quantization of orthogonal dynamics
     Problems
     Bibliographical Notes on Chapter 3

4  Absolute Continuity and Unitary Implementability
     4.1. Introduction
     4.2. Equivalence of distributions
     4.3. Quasi-invarIant distributions and Weyl systems
     4.4. Ergodlclty and irreducibilIty of Weyl pairs
     4.5. Infinite products of HUbert spaces
     4.6. Affine transforms of the isonormal distribution
          Problems
     4.7. Implementability of orthogonal transformations on the fermion field
          Problems
     1981.)Bibliographical Notes on Chapter 4

5  C*-Algebraic Quantization
     5.1. Introduction
     5.2. Weyl algebras over a linear symplectic space
          Problems
     5.3. Regular states of the general boson field
     5.4. The Clifford C*-Algebra
     5.5. Lexicon: The distribution of occupation numbers
          Problems
     Bibliographical Notes on Chapter 5

6  Quantization of Linear Differential Equations
     6.1. Introduction
     6.2. The Sehrodinger equation
     6.3. Quantization of second-order equations
     6.4. Finite propagation velocity
     6.5. Quantlzation of the Dirac equation
     6.6. Quantization of global spaces of wave functions
     Problems
     BIblIographical Notes on Chapter 6

7  Renormalized Products of Quantum Fields
     7.1. The algebra of additive renormalization
     7.2. Renormalized products of the free boson field
          Problems
     7.3. Regularity properties of boson field operators
          Problems
     7.4. Renormalized local products of field operators
     Problems
     Bibliographical Notes on Chapter 7

8  Construction of Nonlinear Quantized Fields
     8.1. IntroductIon
     8.2. The Lp scale
     8.3. Renormalized products at fixed times
          Problems
     8.4. Properties of fixed-time renormalizatlon
          Problems
     8.5. The semigroup generated by the interaction Hamiltonian
     8.6. The pseudo-Interacting field
     8.7. Dynamic causality
     8.8. The local quantized equation of motion
     Problems
     Bibliographical Notes on Chapter 8
Appendix A. Principal Notations
Appendix B. Universal Fields and the Quantization of Wave Equations
Glossary
Bibliography
Index