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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
List 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.
About the author
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.
Summary
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.
Report
'Geometry, Symmetries, and Classical Physics - A Mosaic" by Manousos Markoutsakis is a remarkable journey through the intertwined worlds of geometry and classical physics with a particular focus on symmetries. The author has crafted a book that not only educates but also inspires readers to delve deeper into the profound connections between these fields. One of the strengths of this book is its approachability. The author has described the mathematics behind the subject quite nicely with a great clarity. The book is also made accessible to a wide range of readers, from physics enthusiasts to students and researchers. The book's organization is also a highlight. It leads the reader through a logical progression, building on previously discussed concepts and culminating in a comprehensive understanding of the role of symmetries in classical physics. While the book excels in many aspects, it is worth noting that some sections may challenge readers without a strong mathematical background. However, this should not deter anyone from exploring the book, as the author's explanations and insights are valuable even for those who may not grasp every mathematical detail. Most importantly, the physics behind a mathematical expression is well-described. I think it is a good addition to the literature on physics and geometry. It serves as an enlightening mosaic that beautifully illustrates the profound connections between these fields.'
- Prof. Dr. Taushif Ahmed, Universität Regensburg, September, 2023.
