Overture I: The Universe as a set of harmonic oscillators 1. Lagrangians 2. Simple harmonic oscillators 3. Occupation number representation 4. Making second quantization work II: Writing down Lagrangians 5. Continuous systems 6. A first stab at relativistic quantum mechanics 7. Examples of Lagrangians, or how to write down a theory III: The need for quantum fields 8.
The passage of time 9. Quantum mechanical transformations 10. Symmetry 11. Canonical quantization of fields 12. Examples of canonical quantization 13. Fields with many components and massive electromagnetism 14. Gauge fields and gauge theory 15. Discrete transformations IV: Propagators and perturbations 16.
Ways of doing quantum mechanics: propagators and Green's functions 17. Propagators and Fields 18. The S-matrix 19. Expanding the S-matrix: Feynman diagrams 20. Scattering theory V: Interlude: wisdom from statistical physics 21. Statistical physics: a crash course 22. The generating functional for fields VI: Path Integrals 23. Path Integrals: I said to him, "You're crazy" 24.
Field Integrals 25. Statistical field theory 26. Broken symmetry 27. Coherent states 28. Grassmann numbers: coherent states and the path integral for fermions VII: Topological ideas 29. Topological objects 30. Topological field theory VIII: Renormalization: taming the infinite 31. Renormalization, quasiparticles and the Fermi surface 32.
Renormalization: the problem and its solution 33. Renormalization in action: propagators and Feynman diagrams 34. The renormalization group 35. Ferromagnetism: a renormalization group tutorial IX: Putting a spin on QFT 36. The Dirac equation 37. How to transform a spinor 38. The quantum Dirac field 39. A rough guide to quantum electrodynamics 40.
QED scattering: three famous cross sections 41. The renormalization of QED and two great results X: Some applications from the world of condensed matter 42. Superfluids 43. The many-body problem and the metal 44. Superconductors 45. The fractional quantum Hall fluid XI: Some applications from the world of particle physics 46. Non-abelian gauge theory 47. The Weinberg-Salam model 48.
Majorana fermions 49. Magnetic monopoles 50. Instantons, tunnelling and the end of the world Appendix A: Further reading Appendix B: Useful complex analysis.