9789810226244

Wavelets and Renormalizations

by
  • ISBN13:

    9789810226244

  • ISBN10:

    9810226241

  • Format: Hardcover
  • Copyright: 1999-05-01
  • Publisher: World Scientific Pub Co Inc
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Summary

"the author has succeeded in giving a vivid and pedagogical presentation of a monumental work in recent mathematical physics, illustrating the mutual influence between wavelet analysis and renormalization group techniques of Euclidean field theory."Mathematical Reviews, 2001"This book is a great achievement. It is difficult to read, but very rewarding for those who read it in depth."Monatshefte f r Mathematik, 2001

Table of Contents

Preface ix
Mathematical Sketches of Quantum Physics
1(104)
Measurement and Dynamics
6(5)
Imaginary Time Correlations
11(4)
Correspondence Principle
15(8)
The Harmonic Oscillator
23(7)
The Feynman-Kac Formula
30(6)
Quantum Mechanics of One Relativistic Particle
36(4)
Crisis in the Theory and Formalism
40(7)
Canonical Formalism of Quantum Field Theory
47(9)
Functional Integration for Quantum Field Theory
56(8)
Axiomatic Quantum Field Theory
64(9)
The Constructive Problem
73(9)
A Tale of Two Dimensions
82(15)
The Need for Phase Cell Analysis
97(8)
Wavelets--Basic Theory and Construction
105(74)
The Balian-Low Theorem
110(7)
Lemarie and Meyer Wavelets
117(6)
Daubechies Wavelets
123(8)
Vanishing Moments
131(4)
Uncertainty Relations for (P) = 0 Wavelet States
135(5)
Further Constraints of Heisenberg Type
140(10)
Variational Construction
150(6)
Without Intrascale Orthogonality
156(7)
Chui-Wang Wavelets
163(6)
Multi-Dimensional Wavelets
169(10)
Equilibrium States of Classical Crystals
179(102)
Classical Spin Systems
185(9)
Phase Transitions and Ergodic Decomposition
194(7)
Phase Transitions and Reflection Positivity
201(13)
The Ising Model
214(6)
The Ginzburg-Landau Model
220(8)
Polymer Expansions
228(9)
Expansion for Nearest-Neighbor Interactions
237(7)
Inductive Interpolation
244(10)
A Generalization of the Polymer Estimation
254(3)
Unit-Vector Spins with Long-Range Coupling
257(6)
Combinatorial Properties of Interpolation Weights
263(8)
Scalar Spins with Long Range Coupling
271(4)
Extra 1/N! Factors in the Inductive Expansion
275(6)
A Wavelet Introduction to the Renormalization Group
281(120)
Averaging Transformations
290(7)
The Renormalization Group Transformation
297(6)
Minimizers and Orthogonality
303(7)
Connection to the Continuum Wavelet Cutoff
310(8)
Canonical Wavelet Manifold and ZF Transformation
318(7)
Relevant, Marginal, and Irrelevant Parameters
325(7)
Canonical Inverse-Limit Manifold
332(8)
Wick Ordering and Linearized RG Analysis
340(8)
The Second-Order RG Transformation
348(8)
Wavelet Diagrams
356(4)
The One-Loop-per-Scale Transformation
360(9)
The Wilson Wavelet Recursion Formula
369(7)
The Baker-Dyson-Wilson Hierarchical Model
376(6)
The Hierarchical Model to Second Order
382(7)
Hierarchical One-Loop-per-Scale Transformation
389(5)
Wavelet Correction of the Hierarchical Model
394(7)
Wavelet Analysis of ϕ4/3
401(112)
The Cutoff - A Finite Set of Modes
407(5)
Wavelet Estimates
412(5)
Inductive Operations
417(6)
Estimates on Numerical Factors
423(8)
Expansion Rules and Wavelet Diagrams
431(12)
Organizing the Completed Expansion
443(8)
The Phase Cell Polymer
451(5)
Estimating the Activity I: Stability and Quartic Positivity
456(8)
Estimating the Activity II: Internal Combinatorics
464(7)
Combinatorics for Summing Over Polymers
471(7)
Strategy for Number Divergence Cancellation
478(5)
From Infinitely Many Cases to Finitely Many
483(9)
Wavelet Diagrams for Cases
492(12)
How to Assign Numerical Factors
504(9)
Bibliography 513

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