Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem
Trade Review
'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.
'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.
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.
