CHRIS ISHAM MODERN DIFFERENTIAL GEOMETRY FOR PHYSICISTS PDF

A number of small corrections and additions have also been made. These lecture notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course? Quantum Fields and Fundamental Forces? 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 these days 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. The volume is divided into four parts: i introduction to general topology; ii introductory coordinate-free differential geometry; iii geometrical aspects of the theory of Lie groups and Lie group actions on manifolds; iv introduction to the theory of fibre bundles.

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