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This edition of the invaluable text Modern Differential Geometry for Physicists 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. ## About book:

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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 "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 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. 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. This is done with 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.

- Series:
**World Scientific Lecture Notes in Physics** - Author:
**C. J. Isham** - Year:
**1999** - Publisher:
**World Scientific Publishing Company** - Language:
**English** - ISBN:
**9789810235550,981-02-3555-0**

- File size:
**15 574 749** - Format:
**pdf**

Security code:

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...

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...

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the authorâ€™s perspective is used in this work to describe physical theories of a geometric character without using any no...

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the authorâ€™s perspective is used in this work to describe physical theories of a geometric character without using any no...

This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations i...

Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the c...

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the...

Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has b...

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concep...

A comprehensive review of the effects of cannabinoids on cellular metabolism, reproduction and brain function, containing 50 contributions written by the leading researchers in the field. For the first time the drug is shown to have marked effects on a wh...