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| Preface 1 Mathematical Sketches of Quantum Physics 1.1 Measurement and Dynamics 1.2 Imaginary Time Correlations 1.3 Correspondence Principle 1.4 The Harmonic Oscillator 1.5 The Feynman Kac Formula 1.6 Quantum Mechanics of One Relativistic Particle 1.7 Crisis in the Theory and Formalism 1.8 Canonical Formalism of Quantum Field Theory 1.9 Functional Integration for Quantum Field Theory 1.10 Axiomatic Quantum Field Theory 1.11 The Constructive Problem 1.12 A Tale of Two Dimensions 1.13 The Need for Phase Cell Analysis 2 Wavelets - Basic Theory and Construction 2.1 The Balian Low Theorem 2.2 Lemarie and Meyer Wavelets 2.3 Daubcchies Wavelets 2.4 Vanishing Moments 2.5 Uncertainty Relations for (P) = 0 Wavelet States 2.6 Further Constraints of Heisenberg Type 2.7 Variational Construction 2.8 Without Intrascale Orthogonality 2.9 Chui Wang Wavelets 2.10 Multi-Dimensional Wavelets 3 Equilibrium States of Classical Crystals 3.1 Classical Spin Systems 3.2 Phase Transitions and Ergodie Decomposition 3.3 Phase Transitions and Reflection Positivity 3.4 The Ising Model 3.5 The Ginzburg Landau Model 3.6 Polymer Expansions 3.7 Expansion for Nearest-Neighbor Interactions 3.8 Inductive Interpolation 3.9 A Generalization of the Polymer Estimation 3.10 Unit-Vector Spins with Long-Range Coupling 3.11 Combinatorial Properties of Interpolation Weights 3.12 Scalar Spins with Long Range Coupling 3.13 Extra 1/N! Factors in the Inductive Expansion 4 A Wavelet Introduction to the Renormalization Group 4.1 Averaging Transformations 4.2 The Renormalization Group Transformation 4.3 Minimizers and Orthogonality 4.4 Connection to the Continuum Wavelet Cutoff 4.5 Canonical Wavelet Manifold and ZF Transformation 4.6 Relevant, Marginal, and Irrelevant Parameters 4.7 Canonical Inverse-Limit Manifold 4.8 Wick Ordering and Linearized RG Analysis 4.9 The Second-Order RG Transformation 4.10 Wavelet Diagrams 4.11 The One-Loop-per-Scale Transformation 4.12 The Wilson Wavelet Recursion Formula 4.13 The Baker Dyson Wilson ttierarchical Model 4.14 The Hierarchical Model to Second Order 4.15 Hierarchical One-Loop-per-Scale Transformation 4.16 Wavelet Correction of the Hierarchical Model 5 Wavelet Analysis of 4/3 5.1 The Cutoff - A Finite Set of Modes 5.2 Wavelet Estimates 5.3 Inductive Operations 5.4 Estimates on Numerical Factors 5.5 Expansion Rules and Wavelet Diagrams 5.6 Organizing the Completed Expansion 5.7 The Phase Cell Polymer 5.8 Estimating the Activity h Stability and Quartic Positivity 5.9 Estimating the Activity Ih Internal Combinatories 5.10 Combinatorics for Summing Over Polymers 5.11 Strategy for Number Divergence Cancellation 5.12 From Infinitely Many Cases to Finitely Many 5.13 Wavelet Diagrams for Cases 5.14 How to Assign Numerical Factors Bibliography |
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