| Chapter | Title | Key Topics Covered | | :--- | :--- | :--- | | 1 | Introduction | Symmetry, Quantum Mechanics, and Group Theory in a Nutshell | | 2 | Basic Group Theory | Fundamental definitions, examples of finite and infinite groups | | 3 | Group Representations | Reducible and irreducible representations, character theory | | 4 | General Properties of Irreducible Vectors and Operators | Wigner-Eckart theorem, matrix elements in quantum mechanics | | 5 | Representations of the Symmetric Groups | Young tableaux, permutation groups and their physical applications | | 6 | One-Dimensional Continuous Groups | Rotations, translations, and the generation of Lie groups | | 7 | Rotations in 3D Space: The Group SO(3) | Angular momentum theory, spherical harmonics, rotation matrices | | 8 | The Group SU(2) and More About SO(3) | Spinor representations and the connection between SU(2) and SO(3) | | 9 | Euclidean Groups in 2D and 3D Space | Space groups, crystal symmetries, and translations | | 10 | The Lorentz and Poincaré Groups | Relativistic symmetries and their irreducible representations | | 11 | Space Inversion Invariance | Parity, pseudoscalars, and their role in fundamental interactions | | 12 | Time Reversal Invariance | Anti-linear operators and their consequences in quantum systems | | 13 | Finite-Dimensional Representations of Classical Groups | Unitary groups (U(n), SU(n)) and orthogonal groups (O(n), SO(n)) |
: The mathematical backbone behind calculating quantum transition rates and selection rules.
A quick Google or Reddit search for "Wu-ki Tung Group Theory in Physics pdf free download" may lead to Library Genesis (LibGen), Sci-Hub, or similar shadow libraries. Wu-ki Tung Group Theory In Physics Pdf
The true brilliance of "Group Theory in Physics" lies in its second half, where the abstract mathematics yields profound physical insights. Quantum Mechanics and Angular Momentum
Wu-Ki Tung's approach in the PDF is to introduce group theory in a way that is accessible to physicists, with a focus on the applications in physics. He covers: | Chapter | Title | Key Topics Covered
. This is essential for any physicist studying quantum mechanics, as it dictates the behavior of angular momentum and spin. The chapter thoroughly explores the derivation of Clebsch-Gordan coefficients and the Wigner-Eckart theorem. 5. The Lorentz and Poincaré Groups
: Covers basic group theory (definitions, subgroups, cosets) and the core principles of group representations. Continuous Groups : In-depth treatment of (rotations), , and their roles in angular momentum. Relativistic Symmetries : Detailed exposition of the Lorentz and Poincaré groups Quantum Mechanics and Angular Momentum Wu-Ki Tung's approach
The specific paper often associated with Wu-Ki Tung's foundational work is his book, published by World Scientific.
It doesn’t just teach you what a group is; it teaches you how to think in symmetries. To help you get exactly what you need for your studies:
: Chapters 10–12 (Gauge theories). Here, the book connects to quantum field theory. If you are not yet studying QFT, you can pause. But for particle physicists, this is the payoff.