Includes bibliographical references and index.
Review of linear algebra -- Symmetry and groups -- Finite groups -- Rotation and the notion of Lie algebra -- Representation theory -- Schur's lemma and the great orthogonality theorem -- Character is a function of class -- Real, pseudoreal, complex, and the number of square roots -- Crystals -- Euler, Fermat, and Wilson -- Frobenius groups -- Quantum mechanics and group theory: degeneracy -- Group theory and harmonic motion -- Symmetry in the laws of physics: Lagrangian and Hamiltonian -- Tensors and representations of the rotation groups SO(N) -- Lie algebra of SO(3) and ladder operators: creation and annihilation -- Angular momentum and Clebsch-Gordan decomposition -- Tensors and representations of the unitary groups SU(N) -- SU(2): double covering and the spinor -- The electron spin and Kramer's degeneracy -- Integration over continuous groups, topology, and coset manifolds -- Symplectic groups and their algebras -- From Lagrangian mechanics to quantum field theory: it's but a skip and a hop -- Multiplying irreducible representations of finite groups: return to the tetrahedral group -- Crystal field splitting -- Group theory and special functions -- Covering the tetrahedron -- Isospin and and the discovery of a vast internal space -- The Eightfold Way of SU(3) -- The Lie algebra of SU(3) and its root vectors -- Group theory guides us into the microscopic world -- The poor man finds his roots -- Roots and weights for orthogonal, unitary, and symplectic algebras -- Lie algebras in general -- Killing-Cartan classification -- Dynkin diagrams -- SO(2N) and its spinors -- Galileo, Lorentz, and Poincaré -- SL(2,C) double covers SO(3,1): group theory leads us to the Weyl equation -- From the Weyl equation to the Dirac equation -- Dirac and Majorana spinors: antimatter and pseudoreality -- The hydrogen atom and SO(4) -- The unexpected emergence of the Dirac equation in condensed matter physics -- The even more unexpected emergence of the Majorana equation in condensed matter physics -- Contraction and extension -- Conformal algebra -- The expanding universe and group theory -- The gauged universe -- Grand unification and SU(5) -- From SU(5) to SO(10) -- The family mystery.
"Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been msising is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study"