Lectures On Advanced Mathematical Methods For Physicists - Tapa dura

Mukunda, N; Mukhi, Sunil

9789814299732: Lectures On Advanced Mathematical Methods For Physicists

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ISBN 10: 9814299731 ISBN 13: 9789814299732

Editorial: World Scientific Publishing Co Pte Ltd, 2010

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This book presents a survey of Topology and Differential Geometry and also, Lie Groups and Algebras, and their Representations. The first topic is indispensable to students of gravitation and related areas of modern physics (including string theory), while the second has applications in gauge theory and particle physics, integrable systems and nuclear physics.Part I provides a simple introduction to basic topology, followed by a survey of homotopy. Calculus of differentiable manifolds is then developed, and a Riemannian metric is introduced along with the key concepts of connections and curvature. The final chapters lay out the basic notions of simplicial homology and de Rham cohomology as well as fibre bundles, particularly tangent and cotangent bundles.Part II starts with a review of group theory, followed by the basics of representation theory. A thorough description of Lie groups and algebras is presented with their structure constants and linear representations. Root systems and their classifications are detailed, and this section of the book concludes with the description of representations of simple Lie algebras, emphasizing spinor representations of orthogonal and pseudo-orthogonal groups.The style of presentation is succinct and precise. Involved mathematical proofs that are not of primary importance to physics student are omitted. The book aims to provide the reader access to a wide variety of sources in the current literature, in addition to being a textbook of advanced mathematical methods for physicists.

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Acerca del autor

Charlotte y Peter Fiell son dos autoridades en historia, teor�a y cr�tica del dise�o y han escrito m�s de sesenta libros sobre la materia, muchos de los cuales se han convertido en �xitos de ventas. Tambi�n han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Dise�o del siglo XX, El dise�o industrial de la A a la Z, Scandinavian Design y Dise�o del siglo XXI.

De la contraportada

This book surveys Topology and Differential Geometry and also, Lie Groups and Algebras, and their Representations. The former topic is indispensable to students of gravitation and related areas of modern physics, including string theory. The latter has applications in gauge theory and particle physics, integrable systems and nuclear physics, among many others. The style of presentation is such that the mathematical statements are succinct and precise, but skip involved proofs that are not of primary importance to the physics reader.Part I provides a simple introduction to basic topology, followed by a survey of homotopy. Calculus of differentiable manifolds is developed, after which a Riemannian metric is introduced along with the key concepts of connections and curvature. The final chapters lay out the basic notions of homology and De Rham cohomology as well as fibre bundles, particularly tangent and cotangent bundles.Part II starts with a review of group theory followed by the basics of representation theory. A thorough description of Lie groups and algebras is presented with their structure constants and linear representations. Next, root systems and their classifications are detailed, concluding with the description of representations of simple Lie algebras emphasizing on spinor representations of orthogonal and pseudo-orthogonal groups.

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