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Global Analysis in Mathematical Physics

Geometric and Stochastic Methods

  • Book
  • © 1997

Overview

Authors:
  1. Yuri Gliklikh

    1. Department of Mathematics, Voronezh State University, Voronezh, Russia

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Part of the book series: Applied Mathematical Sciences (AMS, volume 122)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XV
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  2. Finite-Dimensional Differential Geometry and Mechanics

    1. Front Matter

      Pages 1-1
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    2. Some Geometric Constructions in Calculus on Manifolds

      • Yuri Gliklikh
      Pages 3-15

    3. Geometric Formalism of Newtonian Mechanics

      • Yuri Gliklikh
      Pages 17-35

    4. Accessible Points of Mechanical Systems

      • Yuri Gliklikh
      Pages 39-46

  3. Stochastic Differential Geometry and its Applications to Physics

    1. Front Matter

      Pages 47-47
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    2. Stochastic Differential Equations on Riemannian Manifolds

      • Yuri Gliklikh
      Pages 49-85

    3. The Langevin Equation

      • Yuri Gliklikh
      Pages 87-94

    4. Mean Derivatives, Nelson’s Stochastic Mechanics, and Quantization

      • Yuri Gliklikh
      Pages 95-130

  4. Infinite-Dimensional Differential Geometry and Hydrodynamics

    1. Front Matter

      Pages 131-131
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    2. Geometry of Manifolds of Diffeomorphisms

      • Yuri Gliklikh
      Pages 133-146

    3. Lagrangian Formalism of Hydrodynamics of an Ideal Incompressible Fluid

      • Yuri Gliklikh
      Pages 147-170

    4. Hydrodynamics of a Viscous Incompressible Fluid and Stochastic Differential Geometry of Groups of Diffeomorphisms

      • Yuri Gliklikh
      Pages 171-177

  5. Back Matter

    Pages 179-216
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Keywords

About this book

The first edition of this book entitled Analysis on Riemannian Manifolds and Some Problems of Mathematical Physics was published by Voronezh Univer­ sity Press in 1989. For its English edition, the book has been substantially revised and expanded. In particular, new material has been added to Sections 19 and 20. I am grateful to Viktor L. Ginzburg for his hard work on the transla­ tion and for writing Appendix F, and to Tomasz Zastawniak for his numerous suggestions. My special thanks go to the referee for his valuable remarks on the theory of stochastic processes. Finally, I would like to acknowledge the support of the AMS fSU Aid Fund and the International Science Foundation (Grant NZBOOO), which made possible my work on some of the new results included in the English edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian Edition The present book is apparently the first in monographic literature in which a common treatment is given to three areas of global analysis previously consid­ ered quite distant from each other, namely, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me­ chanics, and infinite-dimensional differential geometry of groups of diffeomor­ phisms and hydrodynamics. The unification of these topics under the cover of one book appears, however, quite natural, since the exposition is based on a geometrically invariant form of the Newton equation and its analogs taken as a fundamental law of motion.

Authors and Affiliations

  • Department of Mathematics, Voronezh State University, Voronezh, Russia

    Yuri Gliklikh

Bibliographic Information

  • Book Title: Global Analysis in Mathematical Physics

  • Book Subtitle: Geometric and Stochastic Methods

  • Authors: Yuri Gliklikh

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-1866-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-387-94867-6Published: 13 December 1996

  • Softcover ISBN: 978-1-4612-7317-2Published: 27 September 2012

  • eBook ISBN: 978-1-4612-1866-1Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XV, 216

  • Topics: Global Analysis and Analysis on Manifolds, Theoretical, Mathematical and Computational Physics

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