1st Edition

Geometry, Symmetries, and Classical Physics A Mosaic

By Manousos Markoutsakis Copyright 2022
    482 Pages 43 B/W Illustrations
    by CRC Press

    482 Pages 43 B/W Illustrations
    by CRC Press

    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

    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.


    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.

    '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.