UID:
almafu_9958066808302883
Format:
1 online resource (311 pages)
ISBN:
1-281-76758-1
,
9786611767587
,
0-08-087402-9
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks ; 86
Content:
The main theme of this classic book is the path integral technique and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of Feynman-Kac formula. Starting with main examples of Gaussian processes, the author presents four different proofs of the Feynman-Kac formula.
Note:
Based on lectures given by the author at a consortium in Lausanne, Switzerland, 1977.
,
Front Cover; Functional Integration and Quantum Physics; Copyright Page; Contents; Preface; List of Symbols; Chapter I. Introduction; 1. Introduction; 2. Construction of Gaussian Processes; 3. Some Fundamental Tools of Probability Theory; Chapter II. The Basic Processes; 4. The Wiener Process, the Oscillator Process, and the Brownian Bridge; 5. Regularity Properties-1; 6. The Feynman-Kac Formula; 7. Regularity and Recurrence Properties-2; Chapter III. Bound State Problems; 8. The Birman-Schwinger Kernel and Lieb's Formula; 9. Phase Space Bounds; 10. The Classical Limit
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11. Recurrence and Weak Coupling; Chapter IV. Inequalities; 12. Correlation Inequalities; 13. Other inequalities: Log Concavity, Symmetric Rearrangement, Conditioning, Hypercontractivity; Chapter V. Magnetic Fields and Stochastic Integrals; 14. ltô's Integral; 15. Schrödinger Operators with Magnetic Fields; 16. Introduction to Stochastic Calculus; Chapter VI. Asymptotics; 17. Donsker's Theorem; 18. Laplace's Method in Function Space; 19. Introduction to the Donsker-Varadhan Theory; Chapter VII. Other Topics; 20. Perturbation Theory for the Ground State Energy
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21. Dirichlet Boundaries and Decoupling Singularities in Scattering Theory; 22. Crushed Ice and the Wiener Sausage; 23. The Statistical Mechanics of Charged Particles with Positive Definite Interactions; 24. An Introduction to Euclidean Quantum Field Theory; 25. Properties of Eigenfunctions, Wave Packets, and Green's Functions; 26. Inverse Problems and the Feynman-Kac Formula; References; Index
,
English
Additional Edition:
ISBN 0-12-644250-9
Language:
English
Keywords:
Electronic books
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