Group theory in a nutshell for physicists /

Bibliographic Details
Main Author: Zee, A.
Format: Printed Book
Published: Princeton: Princeton University Press, 2016.
Series:In a nutshell
Subjects:
Group theory.
Online Access:http://www.loc.gov/catdir/enhancements/fy1603/2015037408-d.html
https://www.loc.gov/catdir/enhancements/fy1611/2015037408-b.html
Table of Contents:
  • 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.

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