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
Rezensionen / Stimmen
"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.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Postgraduate and Undergraduate Advanced
Illustrationen
8 s/w Zeichnungen, 8 s/w Abbildungen
8 Line drawings, black and white; 8 Illustrations, black and white
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 16 mm
Gewicht
ISBN-13
978-1-032-13380-5 (9781032133805)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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.
Chapter 1: Differential Forms. Chapter 2: Vector Fields and Their Relationship with Differential Forms. Chapter 3: Aspects of Integration. Chapter 4: The Metric Tensor. Chapter 5: Maxwell's Equations in Terms of Differential Forms. Chapter 6: Classical Mechanics. Chapter 7: Connections. Chapter 8: Generalised Functions From a Geometric Perspective. Appendix A: Solutions and Hints to the Exercises. Suggestions for Further Reading. Index.
