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Introduction to algebraic and constructive quantum field theory
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Contents Preface ix Introduction . xiii 1. The Free Boson Field 3 1.1. Introduction 3 1.2. Weyl and Heisenberg systems 4 1.3. Functional integration 15 1.4. Quasi-invariant distributions 25 1.5. Absolute continuity 30 1.6. Irreducibility and ergodicity 37 1.7. The Fourier-Wiener transform 41 1.8. The structure of T and wave-particle duality 47 1.9. Implications of wave-particle duality 57 1.10. Characterization of the free boson field 62 1.11. The complex wave representation 64 1.12. Analytic features of the complex wave representation 70 2. The Free Fermion Field 75 2.1. Clifford systems 75 2.2. Existence of the free fermion field 80 2.3. The real wave representation 82 2.4. The complex wave representation 89 3. Properties of the Free Fields 96 3.1. Introduction 96 3.2. The exponential laws 97 3.3. irreducMity 99 3.4. Representation of the orthogonal group by measure- preserving transformations . 100 3.5. Bosonic quantization of symplectic dynamics 105 3.6. Fermionic quantization of orthogonal dynamics 113 4. Absolute Continuity and Unitary Implementability 118 4.1. Introduction 118 4.2. Equivalence of distributions 119 4.3. Quasi-invariant distributions and Weyl systems 121 4.4. Ergodicity and irreducibility of Weyl pairs 124 4.5. Infinite products of Hilbert spaces 125 4.6. Affine transforms of the isonormal distribution 130 4.7. Implementability of orthogonal transformations on the fermion field 135 5. C*-Algebraic Quantization 142 5.1. Introduction 142 5.2. Weyl algebras over a linear symplectic space 143 5.3. Regular states of the general boson field 147 5.4. The representation-independent Clifford algebra 149 5.5. Lexicon: The distribution of occupation numbers 150 6. Quantization of Linear Differential Equations 153 6.1. Introduction 153 6.2. The Schrodinger equation 154 6.3. Quantization of second-order equations 158 6.4. Finite propagation velocity 160 6.5. Quantization of the Dirac equation 162 6.6. Quantization of global spaces of wave functions 168 7. Renormalized Products of Quantum Fields 174 7.1. The algebra of additive renormalization 174 7.2. Renormalized products of the free boson field 184 7.3. Regularity properties of boson field operators 190 7.4. Renormalized local products of field operators 200 8. Construction of Nonlinear Quantized Fields 208 8.1. Introduction 208 8.2. The Lp scale 210 8.3. Renormalized products at fixed time 214 8.4. Properties of fixed-time renormalization 223 8.5. The semigroup generated by the interaction Hamiltonian 227 8.6. The pseudo-interacting field 229 8.7. Dynamic causality 233 8.8. The local quantized equation of motion 237 Appendix A Principal Notations 251 Appendix B Universal Fields and the Quantization of Wave Equations 254 Glossary ' 258 Bibliography 281 Index 289 Download link：http://www.isload.com.cn/store/mz5qa54szhav7 [ Last edited by zhq025 on 2008-1-16 at 10:29 ] |
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