Modern Differential Geometry For Physicists: 32 (World Scientific Lecture Notes In Physics) - Softcover

Isham, Chris J

Softcover

ISBN 10: 9971509571 ISBN 13: 9789971509576

Publisher: EPB Publishers Pte Ltd, 1989

Synopsis

These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, non-linear sigma-models and other types of non-linear field systems that feature in modern quantum field theory. This volume is in three parts dealing with, respectively, (i) introductory coordinate-free differential geometry, (ii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, (iii) introduction to the theory of fibre bundles. In the first part of the book the author has laid considerable stress on the basic ideas of "tangent space structure" which he develops from several different points of view: some geometrical, and others more algebraic. This is done with the awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry.

About this title

Review

"The result is a book which provides a rapid initiation to the material in question with care and sufficient detail to allow the reader to emerge with a genuine familiarity with the foundations of these subjects." Mathematical Reviews "This book is carefully written, and attention is paid to rigor and relevant details ... The key notions are discussed with great care and from many points of view, which attenuates the shock of the formalism." Mathematical Reviews

Edition details

• Publisher: EPB Publishers Pte Ltd
• Publication date: 1989
• ISBN 10: 9971509571
• ISBN 13: 9789971509576
• Binding: Paperback
• Language: English
• Number of pages: 192