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.
Manousos Markoutsakis is the Director of AI and HPC (Europe) at DataDirect Networks Inc, where he is responsible for managing the company's engagements in industry and academic institutions. Previously, he worked at IBM, where he was responsible for the company's private-public collaborations in European research and industry. He graduated in physics at the University of Heidelberg, where he worked on nonperturbative QCD. Manousos is a member of the German Physical Society (DPG) and the Bitkom Association.
Chapter 1. Manifolds and Tensors.
Chapter 2. Geometry and Integration on Manifolds.
Chapter 3. Symmetries of Manifolds.
Chapter 4. Newtonian Mechanics.
Chapter 5. Lagrangian Methods and Symmetry.
Chapter 6. Relativistic Mechanics.
Chapter 7. Lie Groups.
Chapter 8. Lie Algebras.
Chapter 9. Representations.
Chapter 10. Rotations and Euclidean Symmetry.
Chapter 11. Boosts and Galilei Symmetry.
Chapter 12. Lorentz Symmetry.
Chapter 13. Poincare Symmetry.
Chapter 14. Conformal Symmetry.
Chapter 15. Lagrangians and Noether's Theorem.
Chapter 16. Spacetime Symmetries of Fields.
Chapter 17. Gauge Symmetry.
Chapter 18. Connection and Geodesics.
Chapter 19. Riemannian Curvature.
Chapter 20. Symmetries of Riemannian Manifolds.
Chapter 21. Einstein's Gravitation.
Chapter 22. Lagrangian Formulation.
Chapter 23. Conservation Laws and Further Symmetries.