Geometry, Symmetries, and Classical Physics

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.

Auteur

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.

Contenu

1. Manifolds and Tensors. 2. Geometry and Integration on Manifolds. 3. Symmetries of Manifolds. 4. Newtonian Mechanics. 5. Lagrangian Methods and Symmetry. 6. Relativistic Mechanics. 7. Lie Groups. 8. Lie Algebras. 9. Representations. 10. Rotations and Euclidean Symmetry. 11. Boosts and Galilei Symmetry. 12. Lorentz Symmetry. 13. Poincare Symmetry. 14. Conformal Symmetry. 15. Lagrangians and Noether's Theorem. 16. Spacetime Symmetries of Fields. 17. Gauge Symmetry. 18. Connection and Geodesics. 19. Riemannian Curvature. 20. Symmetries of Riemannian Manifolds. 21. Einstein's Gravitation. 22. Lagrangian Formulation. 23. Conservation Laws and Further Symmetries.