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David A. Burton received his PhD from Lancaster University, UK, in 2000 and was appointed Lecturer in Physics there in 2005. He is currently Senior Lecturer in Physics at Lancaster. He began his research career in relativistic continuum mechanics and gravitational physics before turning to fluid-structure interactions (in particular, vortex-induced vibration) and, in later years, to relativistic laser-plasma interactions. Adam Noble received his PhD in 2006, also from Lancaster University, and has since held postdoctoral positions at Lancaster and the University of Strathclyde, Scotland, where he is currently a Research Fellow. His interests lie at the interface of physics with geometry, in particular electrodynamics of intense fields, plasma physics and particle physics. The authors maintain a long-standing collaboration and, over the years, have worked on a number of topics connecting electromagnetics, gravitation and plasma physics, including gravitational Sagnac interferometry, relativistic wave-breaking in plasmas, radiation reaction in relativistic plasmas and charged particle beams, and the use of laser-wakefield accelerators in searches for light, weakly-interacting, candidates for dark matter.
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.
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