Quantum Field Theory for the Gifted Amateur

Tom Lancaster, Lecturer in Physics, Department of Physics, University of Durham,Stephen J. Blundell, Professor of Physics, Department of Physics, University of Oxford

Tom Lancaster was a Research Fellow in Physics at the University of Oxford, before becoming a Lecturer at the University of Durham in 2012.


Stephen J. Blundell is a Professor of Physics at the University of Oxford and a Fellow of Mansfield College, Oxford.

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