Global Analysis in Mathematical Physics: Geometric and Stochastic Methods

Hardcover | December 13, 1996

byYuri Gliklikh

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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.

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From Our Editors

This book is the first in monographic literature giving a common treatment to three areas of applications of Global Analysis in Mathematical Physics previously considered quite distant from each other, namely, differential geometry applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanic...

From the Publisher

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 d...

Format:HardcoverDimensions:231 pages, 9.25 × 6.1 × 0.04 inPublished:December 13, 1996Publisher:Springer

The following ISBNs are associated with this title:

ISBN - 10:0387948678

ISBN - 13:9780387948676

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Table of Contents

Contents: Some Geometric Constructions in Calculus on Manifolds.- Geometric Formalism of Newtonian Mechanics.- Accessible Points of Mechanical Systems.- Stocastic Differential Equations on Riemannian Manifolds.- Langevin's Equation.- Mean Derivatives, Nelson's Stochastic Mechanics and Quantization.- 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.

From Our Editors

This book is the first in monographic literature giving a common treatment to three areas of applications of Global Analysis in Mathematical Physics previously considered quite distant from each other, namely, differential geometry applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanics, and infinite-dimensional differential geometry fundamental for hydrodynamics. The unification of these topics is made possible by considering the Newton equation or its natural generalizations and analogues as a fundamental equation of motion. New general geometric and stochastic methods of investigation are developed, and new results on existence, uniqueness, and qualitative behavior of solutions are obtained.