Geometry, Symmetries, and Classical Physics : A Mosaic book cover
1st Edition

Geometry, Symmetries, and Classical Physics
A Mosaic

ISBN 9780367535230
Published December 29, 2021 by CRC Press
482 Pages 43 B/W Illustrations

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Book Description

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

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.

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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.