This book which focusses on mechanics, waves and statistics, describes recent developments in the application of differential geometry, particularly symplectic geometry, to the foundations of broad areas of physics. Throughout the book, intuitive descriptions and diagrams are used to elucidate the mathematical theory. It develops a coordinate-free framework for perturbation theory and uses this to show how underlying symplectic structures arise from physical asymptotes. It describes a remarkable parity between classical mechanics which arises asymptotically from quantum mechanics and classical thermodynamics which arises asymptotically from statistical mechanics. Included here is a section with one hundred unanswered questions for further research.
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"Throughout, intuitive descriptions and diagrams elucidate the mathematical theory. It describes a remarkable parity between classical mechanics which arises asymptotically from quantum mechanics and classical thermodynamics which arises asymptotically from statistical mechanics. Included is a section with one-hundred unanswered questions for further research. This book should be of interest to mathematicians, physicists, and others interested in the foundations of physics." Physics Briefs, 1987
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This thesis presents the underlying theoretical basis for an ambitious program to develop a unified, coordinate-free theory of asymptotic perturbation methods in the three major areas of physics: mechanical systems, wave systems, and statistical systems. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geometric perturbation theory, eikonal waves, dynamical vector field, modulational equations, first jet space, wave action density, eikonal limit, secular perturbation theory, momentum map, asymptotic family, initial torus, unperturbed dynamics, canonical bracket, symplectic structure, wavefront set, coadjoint orbit, coadjoint action, lagrangian submanifolds, adiabatic invariance, conormal bundle, equal area rule, dissipative case, maximum entropy formalism, unperturbed orbits, free rigid body Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lie Poisson, Robert Littlejohn, Richard Montgomery, Physics Figure New!
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Front Cover | Front Flap | Table of Contents | First Pages | Back Flap | Back Cover | Surprise Me!
This thesis presents the underlying theoretical basis for an ambitious program to develop a unified, coordinate-free theory of asymptotic perturbation methods in the three major areas of physics: mechanical systems, wave systems, and statistical systems. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geometric perturbation theory, eikonal waves, dynamical vector field, modulational equations, first jet space, wave action density, eikonal limit, secular perturbation theory, momentum map, asymptotic family, initial torus, unperturbed dynamics, canonical bracket, symplectic structure, wavefront set, coadjoint orbit, coadjoint action, lagrangian submanifolds, adiabatic invariance, conormal bundle, equal area rule, dissipative case, maximum entropy formalism, unperturbed orbits, free rigid body Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lie Poisson, Robert Littlejohn, Richard Montgomery, Physics Figure New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 55
books:
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3
books
cite this book:
- Statistical Physics, Third Edition, Part 1: Volume 5 (Course of Theoretical Physics, Volume 5) by L D Landau on page 408, and Back Matter
- Applications of Dynamics to Physics and Chemistry by Joseph John Thomson on page 160
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter
- Statistical Mechanics (North-Holland Personal Library) by R. Kubo in Back Matter
- Fluids and Plasmas: Geometry and Dynamics (Contemporary Mathematics) by Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie in Back Matter
See all 55 books this book cites
- Essays on Mathematical Robotics (The IMA Volumes in Mathematics and its Applications) (v. 104) by John Baillieul on page 268
- Introduction to Geometry of Manifolds with Symmetry (Mathematics and Its Applications (closed)) by V.V. Trofimov in Back Matter
- The Breadth of Symplectic and Poisson Geometry: Festschrift in Honor of Alan Weinstein (Progress in Mathematics) by Jerrold E. Marsden in Front Matter
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