Book Description
Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Author : Anne Boutet de Monvel
Publisher : Springer Science & Business Media
Page : 471 pages
File Size : 47,63 MB
Release : 2013-11-11
Category : Science
ISBN : 940170693X
Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Author : Paolo Gibilisco
Publisher : Cambridge University Press
Page : 447 pages
File Size : 47,89 MB
Release : 2010
Category : Mathematics
ISBN : 0521896193
An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
Author : G. Giachetta
Publisher : World Scientific
Page : 715 pages
File Size : 13,92 MB
Release : 2005
Category : Science
ISBN : 9812701265
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Author : A. Zee
Publisher : Princeton University Press
Page : 632 pages
File Size : 42,32 MB
Release : 2016-03-29
Category : Science
ISBN : 1400881188
A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)
Author : Bernard F. Schutz
Publisher : Cambridge University Press
Page : 272 pages
File Size : 43,57 MB
Release : 1980-01-28
Category : Science
ISBN : 1107268141
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Author : Anne Boutet de Monvel
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 27,29 MB
Release : 1996-01-31
Category : Science
ISBN : 0792339096
Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Author : Wu-Ki Tung
Publisher : World Scientific
Page : 368 pages
File Size : 49,98 MB
Release : 1985
Category : Science
ISBN : 9971966565
An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet.
Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 41,85 MB
Release : 2013-04-09
Category : Mathematics
ISBN : 1475720637
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Author : Frederick W. Byron
Publisher : Courier Corporation
Page : 674 pages
File Size : 27,23 MB
Release : 2012-04-26
Category : Science
ISBN : 0486135063
Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.
Author : David Hestenes
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 37,66 MB
Release : 1984
Category : Mathematics
ISBN : 9789027725615
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.