Tensors for physics
This book is devoted to a thorough didactic presentation of tensors, which play an important role in Physics in order to describe anisotropic phenomena and their orientational behavior. The rigorous presentation of tensors is done in relationship with their wide applications to Mechanics, Quantum Mechanics, Electrodynamics and Optics, Thermodynamics and Statistical Physics. A particular feature of this volume is the presentation of irreducible tensors, that is, symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Other relevant parts of this book include the dynamics of tensors and the 3D Maxwell equations reformulated in their 4D version, in accord with special relativity. The content of the book is divided into 18 chapters, as follows: 1. Introduction; 2. Basics; 3. Symmetry of Second Rank Tensors, Cross Product; 4. Epsilon-Tensor; 5. Symmetric Second Rank Tensors; 6. Decomposition of Second Rank Tensors; 7. Fields, Spatial Differential Operators; 8. Integration of Fields; 9. Irreducible Tensors; 10. Multipole Potentials; 11. Isotropic Tensors; 12. Integral Formulae and Distribution Functions; 13. Spin Operators; 14. Rotation of Tensors; 15. Liquid Crystals and Other Anisotropic Fluids; 16. Constitutive Relations; 17. Tensor Dynamics; 18. From 3D to 4D: Lorentz Transformation, Maxwell Equations. This volume is very well written and it can be a valuable support to researchers and graduate students in mathematical physics, applied nonlinear analysis and other applied sciences.
scientific article; zbMATH DE number 6375628