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.

Autorentext

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.

Inhalt

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.