A Geometrical Approach to Physics

This book provides an accessible introduction to using the tools of differential geometry to tackle a wide range of topics in physics, with the concepts developed through numerous examples to help the reader become familiar with the techniques.

Physical applications are used to develop the techniques and demonstrate their wide-ranging applicability. Formalism is introduced sparingly and step-by-step, where it is needed, and chapters contain exercises for readers to test their understanding. Worked solutions to the exercises are included.

It is an ideal textbook for advanced undergraduate or postgraduate courses on mathematical methods for physicists, for students whose background is in physics rather than mathematics. It is assumed that the reader has no prior knowledge of mathematical methods beyond the content of a standard undergraduate physics degree.

The purpose of the book is to act as a ?gateway? to more advanced books on the applications of differential geometry in physics. It will also help the reader to better appreciate modern physics research that makes use of differential geometry, and the common features that permeate the discipline as a whole.

Key Features:

• Presents a light and accessible treatment


• Can be used as a textbook for a short course on mathematical methods for physicists


• Accessible to advanced undergraduates and postgraduates whose background is in physics, not mathematics

This book offers a didactic approach to a broad area of physics written in terms of the language of modern differential geometry. Its style is lucid and the breadth of its applications astonishing. It is written for physicists who may want to see such language in action before investing in more advanced treatises on foundational material. The reader is invited to work through a set of exercises after each chapter and consult an appendix that provides solutions and hints. Of particular note is the chapter on generalised functions (Dirac distributions) a subject that is rarely covered properly in many undergraduate courses. This technique (made rigorous by L . Schwarz and A. Lichnerowicz in the last century) is briefly illustrated by deriving the covariant distributional version of Maxwell?s electro-magnetic field equations with sources. The book is short (187 pages) and the suggestions given for further reading could have been considerably longer than the one provided. However, a mathematically inclined graduate student of physics with access to a University library may well find this book of value despite its occasionally breathless approach to modern mathematical physics.

- Robin Tucker, Emeritus Professor of Physics, Lancaster University, June 2024.