内容简介
作者简介
A. Zee is professor of physics at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. His books include &34;Quantum Field Theory in a Nutshell&34;, &34;Einstein Gravity in a Nutshell&34;, and &34;Fearful Symmetry: The Search for Beauty in Modern Physics&34; all Princeton.
本书目录
ContentsPreface xi
A Brief Review of Linear Algebra 1
I Part I: Groups: Discrete or Continuous, Finite or Infinite
I.1 Symmetry and Groups 37
I.2 Finite Groups 55
I.3 Rotations and the Notion of Lie Algebra 70
II Part II: Representing Group Elements by Matrices
II.1 Representation Theory 89
II.2 Schur’s Lemma and the Great Orthogonality Theorem 101
II.3 Character Is a Function of Class 114
II.4 Real, Pseudoreal, Complex Representations, and the Number of Square Roots 136
II.i1 Crystals Are Beautiful 146
II.i2 Euler’s ϕ-Function, Fermat’s Little Theorem, and Wilson’s Theorem 150
II.i3 Frobenius Groups 154
III Part III: Group Theory in a Quantum World
III.1 Quantum Mechanics and Group Theory: Parity, Bloch’s Theorem, and the Brillouin Zone 161
III.2 Group Theory and Harmonic Motion: Zero Modes 168
III.3 Symmetry in the Laws of Physics: Lagrangian and Hamiltonian 176
IV Part IV: Tensor, Covering, and Manifold
IV.1 Tensors and Representations of the Rotation Groups SON 185
IV.2 Lie Algebra of SO3 and Ladder Operators: Creation and Annihilation 203
IV.3 Angular Momentum and Clebsch-Gordan Decomposition 216
IV.4 Tensors and Representations of the Special Unitary Groups SUN 227
IV.5 SU2: Double Covering and the Spinor 244
IV.6 The Electron Spin and Kramer’s Degeneracy 255
IV.7 Integration over Continuous Groups, Topology, Coset Manifold, and SO4 261
IV.8 Symplectic Groups and Their Algebras 277
IV.9 From the Lagrangian to Quantum Field Theory: It Is but a Skip and a Hop 283
IV.i1 Multiplying Irreducible Representations of Finite Groups: Return to the Tetrahedral Group 289
IV.i2 Crystal Field Splitting 292
IV.i3 Group Theory and Special Functions 295
IV.i4 Covering the Tetrahedron 299
V Part V: Group Theory in the Microscopic World
V.1 Isospin and the Discovery of a Vast Internal Space 303
V.2 The Eightfold Way of SU3 312
V.3 The Lie Algebra of SU3 and Its Root Vectors 325
V.4 Group Theory Guides Us into the Microscopic World 337
VI Part VI: Roots, Weights, and Classification of Lie Algebras
VI.1 The Poor Man Finds His Roots 347
VI.2 Roots and Weights for Orthogonal, Unitary, and Symplectic Algebras 350
VI.3 Lie Algebras in General 364
VI.4 The Killing-Cartan Classification of Lie Algebras 376
VI.5 Dynkin Diagrams 384
VII Part VII: From Galileo to Majorana
VII.1 Spinor Representations of Orthogonal Algebras 405
VII.2 The Lorentz Group and Relativistic Physics 428
VII.3 SL2,C Double Covers SO3,1: Group Theory Leads Us to the Weyl Equation 450
VII.4 From the Weyl Equation to the Dirac Equation 468
VII.5 Dirac and Majorana Spinors: Antimatter and Pseudoreality 482
VII.i1 A Hidden SO4 Algebra in the Hydrogen Atom 491
VII.i2 The Unexpected Emergence of the Dirac Equation in Condensed Matter Physics 497
VII.i3 The Even More Unexpected Emergence of the Majorana Equation in Condensed Matter Physics 501
VIII Part VIII: The Expanding Universe
VIII.1 Contraction and Extension 507
VIII.2 The Conformal Algebra 515
VIII.3 The Expanding Universe from Group Theory 523
IX Part IX: The Gauged Universe
IX.1 The Gauged Universe 531
IX.2 Grand Unification and SU5 541
IX.3 From SU5 to SO10 550
IX.4 The Family Mystery 560
Epilogue 565
Timeline of Some of the People Mentioned 567
Solutions to Selected Exercises 569
Bibliography 581
Index 583
Collection of Formulas 601
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