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Preface vii
Chapter 1. Relativistic Transformation Laws 4
1-1. Super-Selection Rules 5
1-2. Symmetry Operations 7
1-3. The Lorentz and Poincare Groups 9
1-4. Relativistic Transformation Laws of States 21
Bibliography 30
Chapter 2. Some Mathematical Tools 31
2-1. Definition of Distribution 31
2-2. Fourier Transforms 43
2-3. Laplace Transforms and Holomorphic Functions 47
2-4. Tubes and Extended Tubes 63
2-5. The Edge of the Wedge Theorem 74
2-6. Hilbert Space 84
Bibliography 93
Chapter 3. Fields and Vacuum Expectation Values 96
3-1. Axioms for the Notions of Field and Field Theory 96
3-2. Independence and Compatibility of the Axioms 102
3-3. Properties of the Vacuum Expectation Values 106
3-4. The Reconstruction Theorem: Recovery
of a Theory from its Vacuum Expectation Values 117
3-5. Symmetries in a Field Theory 132
Bibliography
Chapter 4. Some General Theorems of Relativistic
Quantum Field Theory 134
4-1. The Global Nature of Local Commutativity 134
4-2. Properties of the Polynomial Algebra of an Open Set 137
4-3. The PCT Theorem 142
4-4. Spin and Statistics 146
4-5. Haag's Theorem and Its Generalizations 161
4-6. Equivalence Classes of Local Fields (Borchers Classes) 168
Bibliography 175
Appendix 179
Constructive Quantum Field Theory and
the Existence of Non-Trivial Theories of Interacting Fields 179
Local Algebras and Superselection Sectors 191
Bibliography 198
Index 205
Library of Congress Subject Headings for this publication: Quantum field theory