These lecture notes are the content of an introductory course on modern, co-ordinate-free differential geometry which is taken by 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 bearing in mind the way in which differential geometry is applied to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory. This edition of the text contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made. The volume is divided into four parts.
The first provides an introduction to general topology, the second covers introductory co-ordinate-free differential geometry, the third examines geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, and the fourth provides an introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic.
"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
Series: World Scientific Lecture Notes in Physics
Number Of Pages: 304
Published: 1st June 1999
Country of Publication: SG
Dimensions (cm): 22.23 x 15.88
Weight (kg): 0.43
Edition Number: 2
Edition Type: Revised