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Table of contents
Lie Algebras for Mathematical Physics
From vector spaces and brackets to symmetry, representations, and quantum applications
Read each section in order. Every title can be opened as a TheoryTrace document.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: Symmetry, Infinitesimals, and the Idea of a Lie Algebra5
- Chapter 2: Linear Algebra Foundations6
- Chapter 3: The Definition of a Lie Algebra7
- Chapter 4: First Examples and Their Meaning8
- Chapter 5: The Jacobi Identity and Commutator Geometry9
- Chapter 6: From Lie Groups to Lie Algebras10
- Chapter 7: The Exponential Map and the Baker-Campbell-Hausdorff Formula11
- Chapter 8: Representations and Modules12
- Chapter 9: The Adjoint Representation, Derivations, and Automorphisms13
- Chapter 10: Solvable and Nilpotent Lie Algebras14
- Chapter 11: Semisimple Lie Algebras and the Killing Form15
- Chapter 12: Cartan Subalgebras and Root Decompositions16
- Chapter 13: Root Systems, Weyl Groups, and Dynkin Diagrams17
- Chapter 14: Classification of Complex Semisimple Lie Algebras18
- Chapter 15: Highest-Weight Theory19
- Chapter 16: The Universal Enveloping Algebra20
- Chapter 17: Casimir Operators and Invariant Theory21
- Chapter 18: Compact Lie Algebras and Unitary Representations22
- Chapter 19: Real Forms and Noncompact Lie Algebras23
- Chapter 20: Lie Algebras in Classical Mechanics and Field Theory24
- Chapter 21: Lie Algebras in Quantum Mechanics25
- Chapter 22: The Poincare Algebra and Spacetime Symmetry26
- Chapter 23: Gauge Algebras and the Standard Model27
- Chapter 24: Advanced Directions and Research-Level Bridges28
- Conclusion29