ABSTRACT
This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics.
Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume.
Key features:
- Contains a modern, streamlined presentation of classical topics, which are normally taught separately
- Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity
- Focuses on the clear presentation of the mathematical notions and calculational technique
TABLE OF CONTENTS
part I|64 pages
Geometric Manifolds
part II|56 pages
Mechanics and Symmetry
part III|102 pages
Symmetry Groups and Algebras
part IV|54 pages
Classical Fields
part V|52 pages
Riemannian Geometry
part VI|68 pages
General Relativity and Symmetry