دانلود کتاب Stochastic Mechanics. The Unification of Quantum Mechanics with Brownian Motion

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Preface
Contents
About the Author
1 Introduction
1.1 A Brief History
1.2 Diffusion Theories
1.3 The Wick Rotation
1.4 Stochastic Mechanics
1.5 Time Reversibility
1.6 Hidden Variables
1.7 Outline for the Book
2 Classical Dynamics on mathbbRd
3 Stochastic Dynamics on mathbbRd
3.1 The Stochastic Law
3.2 Stochastic Phase Space
3.3 Stochastic Action
3.4 Stochastic Euler-Lagrange Equations
3.5 Boundary Conditions
3.6 The Momentum Process
3.7 Stochastic Hamilton-Jacobi Equations
3.8 Diffusion Equations
4 Complex Stochastic Dynamics on mathbbRd
4.1 Stochastic Action
4.2 Equations of Motion
4.3 Boundary Conditions
4.4 Diffusion Equations
5 Relativistic Stochastic Dynamics on mathbbRd,1
5.1 Equations of Motion
5.2 Diffusion Equations
6 Stochastic Dynamics on Pseudo-Riemannian Manifolds
6.1 Second Order Phase Space
6.2 Equations of Motion
6.3 Hamilton-Jacobi Equations
6.4 Diffusion Equations
6.5 Spacetime Symmetries
7 Stochastic Interpretation
7.1 Locality
7.2 Causality
7.3 Bell\'s Theorem
7.4 The Quantum Foam
8 Discussion
8.1 Conclusion
8.2 Outlook
Appendix A Review of Probability Theory
A.1 Probability Spaces
A.2 Random Variables
A.3 Expectation Value
A.4 Conditional Expectation
A.5 Change of Measure
A.6 L2-spaces
A.7 Generating Functions
Appendix B Review of Stochastic Processes
B.1 Stochastic Processes
B.2 Conditioning
B.3 Stopping Times
B.4 Semi-Martingales
B.5 Markov Processes
B.6 Quadratic Variation
B.7 Lévy Processes
B.8 Wiener Processes
B.9 L2-spaces
B.10 Generating Functionals
Appendix C Review of Stochastic Calculus
Appendix D Second Order Geometry
D.1 Maps Between First and Second Order Geometry
D.2 The Second Order Tangent Bundle
D.3 Stochastic Integration on Manifolds
Appendix E Construction of the Itô Lagrangian
Appendix F Stochastic Variational Calculus
F.1 Stratonovich-Euler-Lagrange Equations
F.2 Itô-Euler-Lagrange Equations
F.3 Hamilton-Jacobi-Bellman Equations
Appendix References