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Functional integration and quantum physics
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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 Download link：http://www.isload.com.cn/store/ezydckz7wtiso [ Last edited by zhq025 on 2008-1-16 at 10:32 ] |
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