Synopses & Reviews
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms.
About the Author
Bernard Schutz has done research and teaching in general relativity and especially its applications in astronomy since 1970. He is an author of more than 170 publications, including three highly-regarded books published by Cambridge University Press: Geometrical Methods of Mathematical Physics, A First Course in General Relativity, and Gravity From the Ground Up. Schutz currently specialises in gravitational wave research, studying the theory of potential sources and designing new methods for analysing the data from current and planned detectors. He is a member of most of the current large-scale gravitational wave projects: GEO600 (operated by the AEI), LIGO, and LISA. Schutz is a Director of the Max Planck Institute for Gravitational Physics, also known as the Albert Einstein Institute (AEI), in Potsdam, Germany. He holds a part-time chair in Physics and Astronomy at Cardiff University, Wales, as well as Honorary Professorships at Potsdam and Hanover universities in Germany. Born and educated in the USA, he taught physics and astronomy for twenty years at Cardiff before moving to Germany. In 1998 he founded the open-access online journal Living Reviews in Relativity. In 2006 he was awarded the Amaldi Gold Medal of the Italian Society for Gravitation (SIGRAV). He is a Fellow of the American Physical Society and of the Institute of Physics, and a member of the German Academy of Natural Sciences Leopoldina and of the Royal Society of Arts and Sciences Uppsala.
Table of Contents
Preface; 1. Some basic mathematics; 2. Differentiable manifolds and tensors; 3. Lie derivatives and Lie groups; 4. Differential forms; 5. Applications in physics; 6. Connections for Riemannian manifolds and gauge theories; Appendix; Notation; Index.