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From the back cover: "A particular aim [of this book] is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulations found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory.
"Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for good practice in applying the presented definitions and techniques. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook."
BRIEF CONTENTS
Part I - Linear Algebra and Tensors
A Quick Introduction to Tensors
Vector Spaces
Tensors
Part II - Group Theory
Groups, Lie Groups, and Lie Algebras
Basic Representation Theory
The Wigner-Eckart Theorm and Other Applications
The book ends with an Appendix (Complexification of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R Representations), References, and an Index.
