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Author : Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Publisher : Unknown
Page : 380 pages
File Size : 49,5 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 0817672311
Author : Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 41,5 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780817647353
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2011
Category : Electronic
ISBN : 1282973622
Author : Ralph M. Kaufmann,Martin Markl,Alexander A. Voronov
Publisher : Unknown
Page : 0 pages
File Size : 50,9 Mb
Release : 2024
Category : Algebraic topology
ISBN : 1470471426
Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 55,9 Mb
Release : 2009-08-17
Category : Mathematics
ISBN : 9783642005411
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Author : Robert Hermann
Publisher : Math Science Press
Page : 363 pages
File Size : 46,9 Mb
Release : 1991
Category : Mathematics
ISBN : 0915692422
VOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9789814467469
Author : U Bruzzo,V. Gorini,U. Moschella
Publisher : CRC Press
Page : 282 pages
File Size : 50,9 Mb
Release : 2002-11-05
Category : Science
ISBN : 9781420034295
Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theo
Author : Michael Francis Atiyah
Publisher : Cambridge University Press
Page : 112 pages
File Size : 55,7 Mb
Release : 1990-08-23
Category : Mathematics
ISBN : 0521395542
These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
Author : James D. Stasheff,John McCleary
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 46,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809136
Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas. It's features include: accessible to a broad audience interested in mathematics and physics; offers a comprehensive overview of Stasheff's work; and, contains papers on very current research topics, including operads, combinatorial polyhedra and moduli spaces.
Author : Anonim
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 43,6 Mb
Release : 1999
Category : Homotopy theory
ISBN : 0821855638
Author : Stancho Dimiev,Kouei Sekigawa
Publisher : World Scientific
Page : 248 pages
File Size : 48,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812704191
The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers.
Author : José F. Cariñena,Alberto Ibort,Giuseppe Marmo,Giuseppe Morandi
Publisher : Springer
Page : 739 pages
File Size : 53,7 Mb
Release : 2014-09-23
Category : Science
ISBN : 9789401792202
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Publisher : American Mathematical Society
Page : 250 pages
File Size : 53,8 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 : Springer
Page : 354 pages
File Size : 48,8 Mb
Release : 2015-01-13
Category : Mathematics
ISBN : 9789462390737
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational sequence theory and its consequences for the global inverse problem (cohomology conditions)- examples of variational functionals of mathematical physics. Complete formulations and proofs of all basic assertions are given, based on theorems of global analysis explained in the Appendix.
