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zhq025

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[资源] Functional integration and quantum physics

Contents

Preface vii
List of Symbols ix
I Introduction
1. Introduction 1
2. Construction of Gaussian Processes 8
3. Some Fundamental Tools of Probability Theory 17
II The Basic Processes
4. The Wiener Process, the Oscillator Process,
and the Brownian Bridge 32
5. Regularity Properties—1 43
6. The Feynman-Kac Formula 48
7. Regularity and Recurrence Properties—2 60
III Bound State Problems
8. The Birman-Schwinger Kernel and Lieb's Formula 88
9. Phase Space Bounds 93
10. The Classical Limit 105
11. Recurrence and Weak Coupling 114
IV Inequalities
12. Correlation Inequalities 119
13. Other Inequalities: Log Concavity, Symmetric
Rearrangement, Conditioning, Hypercontractivity 136
V Magnetic Fields and Stochastic Integrals
14. Ito's Integral 148
15. Schrodinger Operators with Magnetic Fields 159
16. Introduction to Stochastic Calculus 170
VI Asymptotics
17. Donsker's Theorem 174
18. Laplace's Method in Function Space 181
19. Introduction to the Donsker-Varadhan Theory 198
VII Other Topics
20. Perturbation Theory for the Ground State Energy 211
21. Dirichlet Boundaries and Decoupling Singularities
in Scattering Theory 224
22. Crushed Ice and the Wiener Sausage 231
23. The Statistical Mechanics of Charged Particles
with Positive Definite Interactions 245
24. An Introduction to Euclidean Quantum Field
Theory 252
25. Properties of Eigenfunctions, Wave Packets,
and Green's Functions 258
26. Inverse Problems and the Feynman-Kac Formula 272
References 279
Index 293

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[ Last edited by zhq025 on 2008-1-16 at 10:32 ]

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