Markoutsakis M. Geometry, Symmetries, and Classical Physics: A Mosaic

CRC Press, 2022. — 482 p. — ISBN 978-0-367-53523-0.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.Geometric Manifolds
Manifolds and Tensors
Geometry and Integrationon Manifolds
Symmetries of Manifolds
Mechanicsand Symmetry
Newtonian Mechanics
Lagrangian Methods and Symmetry
Relativistic Mechanics
Symmetry Groups and Algebras
Lie Groups
Lie Algebras
Representations
Rotations and Euclidean Symmetry
Boostsand Galilei Symmetry
Lorentz Symmetry
Poincar eSymmetry
Conformal Symmetry
Classical Fields
Lagrangians and Noether's Theorem
Spacetime Symmetriesof Fields
Gauge Symmetry
Riemannian Geometry
Connection and Geodesics
Riemannian Curvature
Symmetries of Riemannian Manifolds
General Relativity and Symmetry
Einstein's Gravitation
Lagrangian Formulation
Conservation Laws and Further Symmetries
Appendices
Notation andConventions
Mathematical Tools
Weyl Rescaling Formulae
Spaces and Symmetry Groups