Geometric Perturbation Theory In Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Perturbation Theory In Physics write by S M Omohundro. This book was released on 1986-10-31. Geometric Perturbation Theory In Physics available in PDF, EPUB and Kindle. 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.
Geometric Perturbation Theory in Physics
Geometric Perturbation Theory in Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Perturbation Theory in Physics write by Stephen Malvern Omohundro. This book was released on 1986. Geometric Perturbation Theory in Physics available in PDF, EPUB and Kindle. 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.
Geometric Perturbation Theory and Plasma Physics
Geometric Perturbation Theory and Plasma Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Perturbation Theory and Plasma Physics write by . This book was released on 1985. Geometric Perturbation Theory and Plasma Physics available in PDF, EPUB and Kindle. Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Geometric Perturbation Theory and Plasma Physics
Geometric Perturbation Theory and Plasma Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Perturbation Theory and Plasma Physics write by Stephen Malvern Omohundro. This book was released on 1985. Geometric Perturbation Theory and Plasma Physics available in PDF, EPUB and Kindle.
Differential Geometric Methods in Theoretical Physics
Differential Geometric Methods in Theoretical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometric Methods in Theoretical Physics write by Ling-Lie Chau. This book was released on 2013-06-29. Differential Geometric Methods in Theoretical Physics available in PDF, EPUB and Kindle. After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit ful again. Many of the leading specialists of both fields became involved in this devel opment. This process even led to the discovery of previously unsuspected connections between various subfields of physics and mathematics. In mathematics this concerns in particular knots von Neumann algebras, Kac-Moody algebras, integrable non-linear partial differential equations, and differential geometry in low dimensions, most im portantly in three and four dimensional spaces. In physics it concerns gravity, string theory, integrable classical and quantum field theories, solitons and the statistical me chanics of surfaces. New discoveries in these fields are made at a rapid pace. This conference brought together active researchers in these areas, reporting their results and discussing with other participants to further develop thoughts in future new directions. The conference was attended by SO participants from 15 nations. These proceedings document the program and the talks at the conference. This conference was preceded by a two-week summer school. Ten lecturers gave extended lectures on related topics. The proceedings of the school will also be published in the NATO-AS[ volume by Plenum. The Editors vii ACKNOWLEDGMENTS We would like to thank the many people who have made the conference a success. Furthermore, ·we appreciate the excellent talks. The active participation of everyone present made the conference lively and stimulating. All of this made our efforts worth while.
