Global Analysis in Mathematical Physics - Geometric and Stochastic Models

This book gives a common treatment to three areas of application of Global analysis to Mathematical Physics previously considered quite distant from each other. These areas are the geometry of manifolds applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanics, and infinite-dimensional differential geometry fundamental for hydrodynamics.

Contents

Preface

Part I : Finite-Dimensional Differential Geometry and Mechanics

• Some Geometric Constructions in Calculus on Manifolds.
• Geometric Formalism of Newtonian Mechanics.
• Accessible Points of Mechanical Systems.

Part II : Stochastic Differential Geometry and its Applications to Physics

• Stocastic Differential Equations on Riemannian Manifolds.
• Langevin's Equation.
• Mean Derivatives, Nelson's Stochastic Mechanics and Quantization.

Part III : Infinite-Dimensional Differential Geometry and Hydrodynamics

• Geometry of Manifolds of Diffeomorphisms.
• Lagrangian Formalism of Hydrodynamics of an Ideal Incompressible Fluid.
• Hydrodynamics of a Viscous Incompressible Fluid and Stochastic Differential Geometry of Groups of Diffeomorphisms.

Appendices
References
Index