A Geometrical Approach to Physics

"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.

"The book strikes an excellent balance between mathematical rigour, pedagogical exposition and clarity, and strong physical grounding. Complex geometrical concepts are introduced systematically, with sufficient detail to ensure understanding without overwhelming the reader, and an excellent number of useful exercises are presented with hints or solutions available. This scaffolding for self-learning is invaluable in a field where intuitive understanding often comes after significant mathematical groundwork, making this an outstanding choice I have no hesitation in recommending for advanced undergraduates and postgraduate students venturing into the beautiful and complex world where geometry meets physics."

- Timothy J. Walton, Senior Lecturer in Applied Mathematics, University of Lancashire, July 2025.