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Author : L. Francaviglia M. Alvarez-Gaume,E. Gherardelli F. Arbarello,C. De Concini
Publisher : Unknown
Page : 204 pages
File Size : 40,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662172933
Author : L. Alvarez-Gaume,E. Arbarello,C. De Concini,N.J. Hitchin
Publisher : Springer
Page : 200 pages
File Size : 43,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468134
Author : I︠U︡. E. Gliklikh
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 45,7 Mb
Release : 1997
Category : Mathematics
ISBN : 0387948678
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.
Author : Yuri Gliklikh
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461218661
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.
Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Publisher : American Mathematical Society
Page : 250 pages
File Size : 49,6 Mb
Release : 2023-08-21
Category : Mathematics
ISBN : 9781470471477
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.
Author : Demeter Krupka
Publisher : Elsevier
Page : 500 pages
File Size : 44,6 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080954286
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Author : Jurij E. Gliklich,Yu. E. Gliklikh
Publisher : Unknown
Page : 213 pages
File Size : 49,9 Mb
Release : 1993
Category : Differentialgeometrie - Hydrodynamik
ISBN : 3540548084
Author : Demeter Krupka,David Saunders
Publisher : Elsevier
Page : 1243 pages
File Size : 44,6 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 9780080556734
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Author : Daqian Li
Publisher : World Scientific
Page : 196 pages
File Size : 51,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9810230249
This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work. The subjects covered by this collection are closely related to differential geometry, partial differential equations and mathematical physics ? the major areas in which Professor Gu has received notable achievements. Many distinguished mathematicians all over the world contributed their papers to this collection. This collection also consists of ?Gu Chaohao and I? written by C N Yang, ?The academic career and accomplishment of Professor Gu Chaohao? by T T Li and ?List of publications of Professor Gu Chaohao?.
Author : Robert Everist Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 688 pages
File Size : 42,5 Mb
Release : 1993-03-29
Category : Mathematics
ISBN : 0821868233
The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge
Author : Kai S Lam
Publisher : World Scientific Publishing Company
Page : 852 pages
File Size : 42,5 Mb
Release : 2015-09-17
Category : Science
ISBN : 9789814667821
This new (second) edition contains a general treatment of quantum field theory (QFT) in a simple scalar field setting in addition to the modern material on the applications of differential geometry and topology, group theory, and the theory of linear operators to physics found in the first edition. All these are introduced without assuming more background on the part of the reader than a good foundation in undergraduate (junior) level mathematical physics. The new material entirely focuses on an introduction to quantum field theory, emphasizing the Feynman path (functional integral) approach to QFT and the renormalization group. With respect to the latter, the focus is on an introduction of its application to critical phenomena in statistical physics, following the outgrowth of the Callan–Symanzik equation originally developed in the context of high energy physics, and the seminal contributions of Kenneth Wilson. One of the overriding aims of the new material is also to draw students' attention to the deep connections between high energy physics and statistical mechanics. The unavoidable technical aspects are explained with a minimum of prerequisite material and jargon, and conceptual understanding is always given prominence before mastery of technical details, but the importance of the latter is never underestimated. Derivational details and motivational discussions are provided in abundance in order to ensure continuity of reading, and to avoid trying the readers' patience.
Author : Gerd Rudolph,Matthias Schmidt
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 50,9 Mb
Release : 2012-11-09
Category : Science
ISBN : 9789400753457
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Author : Ilka Agricola,Thomas Friedrich
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 51,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829516
The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.
Author : Vicente Cortés,Klaus Kröncke,Jan Louis
Publisher : Springer
Page : 121 pages
File Size : 53,8 Mb
Release : 2018-12-05
Category : Mathematics
ISBN : 9783030011260
This book consists of two lecture notes on geometric flow equations (O. Schnürer) and Lorentzian geometry - holonomy, spinors and Cauchy Problems (H. Baum and T. Leistner) written by leading experts in these fields. It grew out of the summer school “Geometric flows and the geometry of space-time” held in Hamburg (2016) and provides an excellent introduction for students of mathematics and theoretical physics to important themes of current research in global analysis, differential geometry and mathematical physics
Author : Wang Rong,Chen Yue
Publisher : World Scientific
Page : 222 pages
File Size : 50,7 Mb
Release : 1999-01-18
Category : Mathematics
ISBN : 9789814495806
This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics.