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| Author | : V. V. Dodonov |
| Publisher | : Nova Science Publishers |
| Total Pages | : 342 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Alexey P Isaev |
| Publisher | : World Scientific |
| Total Pages | : 475 |
| Release | : 2018-03-22 |
| Genre | : Science |
| ISBN | : 9813236876 |
The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence.The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics.
| Author | : V. V. Dodonov |
| Publisher | : |
| Total Pages | : |
| Release | : 1991 |
| Genre | : Mathematical physics |
| ISBN | : 9781560720379 |
| Author | : Muthuswamy Lakshmanan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 219 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642760465 |
Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989
| Author | : Palash B. Pal |
| Publisher | : Cambridge University Press |
| Total Pages | : 717 |
| Release | : 2019-05-23 |
| Genre | : Science |
| ISBN | : 1108492207 |
Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.
| Author | : Graham S Hall |
| Publisher | : World Scientific |
| Total Pages | : 443 |
| Release | : 2004-04-27 |
| Genre | : Science |
| ISBN | : 9814505315 |
This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.
| Author | : V. V. Dodonov |
| Publisher | : Nova Publishers |
| Total Pages | : 300 |
| Release | : 1991 |
| Genre | : Science |
| ISBN | : |
| Author | : P.H. Kersten |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9400901798 |
The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.
| Author | : Heinz-dietrich Doebner |
| Publisher | : World Scientific |
| Total Pages | : 446 |
| Release | : 1994-07-05 |
| Genre | : |
| ISBN | : 9814550884 |
This volume contains material submitted to a symposium on mathematical physics in July 1993 at the Technical University of Clausthal. It focuses on mathematical and physical notions of symmetries, especially on generalized and quantum symmetries (quantum groups and algebras) with applications to integrable systems, quasi-exact solvability, quantization methods and nonlinear problems. The workshop is a continuation of the series of meetings and workshops on mathematical physics in Clausthal which brings together mathematicians, theoretical and mathematical physicists working in the different parts of generalized symmetries. Recent developments in the mathematical structure and physical applications of generalized symmetries are discussed.
| Author | : Palash B. Pal |
| Publisher | : Cambridge University Press |
| Total Pages | : 718 |
| Release | : 2019-05-23 |
| Genre | : Science |
| ISBN | : 1108661394 |
An algebraic structure consists of a set of elements, with some rule of combining them, or some special property of selected subsets of the entire set. Many algebraic structures, such as vector space and group, come to everyday use of a modern physicist. Catering to the needs of graduate students and researchers in the field of mathematical physics and theoretical physics, this comprehensive and valuable text discusses the essential concepts of algebraic structures such as metric space, group, modular numbers, algebraic integers, field, vector space, Boolean algebra, measure space and Lebesgue integral. Important topics including finite and infinite dimensional vector spaces, finite groups and their representations, unitary groups and their representations and representations of the Lorentz group, homotopy and homology of topological spaces are covered extensively. Rich pedagogy includes various problems interspersed throughout the book for better understanding of concepts.
