【目次】 1 Global properties of groups and Lie groups 1.1 Groups 1.2 Topological groups 1.3 Lie groups: global considerations
2 Local properties of Lie groups 2.1 Structure functions and structure constants 2.2 Differential forms 2.3 Parameter transformations 2.4 Local Lie groups and Lie algebras 2.5 Conjugation and adjoint representation
3 Lie algebras 3.1 General properties of Lie algebras 3.2 The Cartan metric 3.3 The adjoint representation of the algebra 3.4 Compact Lie algebras 3.5 Cartan canonical form of simple compact Lie algebras 3.6 Root diagrams and the Weyl group 3.7 Primitive roots, Dynkin diagrams and classification
4 Hermitian irreducible representations of compact simple Lie algebras 4.1 Weight diagrams, dominant and highest weights 4.2 Multiplicities of internal weights 4.3 The dual of the root lattice. Primitive weights 4.4 Fundamental tensor (single-valued) representations 4.5 Fundamental spinor representations 4.6 Diagrammatic representation of the Dynkin indices
5 Continuous unitary irreducible representations (CUIRs) of compact Lie groups 5.1 Representations of Lie groups 5.2 Linear representations of compact Lie groups 5.3 Global properties of the representations: true groups 5.4 Reality properties of the CUIRs 5.5 Dimension of the CUIRs 5.6 Casimir invariants and indices
6 Rigid internal groups 6.1 Introduction 6.2 Noether currents 6.3 Application of the rigid internal groups 6.4 The quark model of the elementary fields
7 The gauge principle 7.1 Introduction 7.2 Electromagnetism 7.3 The gauge principle for simple Lie groups 7.4 Renormalization constraints: the axial anomaly 7.5 Renormalization constraints: asymptotic freedom
8 Spontaneous symmetry breaking 8.1 Motivation and definition 8.2 Gauge field sector of L(Aμ, ψ, θ) 8.3 Scalar-Fermion sector 8.4 The Goldstone theorem and the scalar potential 8.5 Higgs mechanism 8.6 Completeness of the Higgs mechanism
9 Gauge theory of the non-gravitational interactions 9.1 Introduction 9.2 Gauge theory of the strong interactions 9.3 Standard model of the weak and electromagnetic interactions 9.4 S(U(3) x U(2)) theory of the non-gravitational interactions: generations
10 Grand unification 10.1 Introduction 10.2 Renormalization group preliminary 10.3 Minimal GUT (G = SU(5)) 10.4 SO(10) GUT model 10.5 Ground rules for GUT models 10.6 Models without horizontal symmetry 10.7 Models with horizontal (and other) symmetries 10.8 Pros and cons of grand unification
11 Orbit structure 11.1 Introduction 11.2 SU(2) orbits 11.3 Orbits for first- and second-rank tensors of SO(n) 11.4 Orbits for first- and second-rank tensors of SU(n) 11.5 Symmetric algebras; adjoint of SU(n) 11.6 General orbital structure 11.7 Orbits and invariants
12 The scalar potential 12.1 General considerations 12.2 Examples for irreducible representations 12.3 Example for a reducible representation 12.4 Goldstone structure for a two-stage symmetry breakdown 12.5 The gauge hierarchy problem