# Quantum Field Theory for the Gifted Amateur

**by**Lancaster, Tom; Blundell, Stephen J.

### 9780199699339

019969933X

Paperback

6/17/2014

Oxford University Press

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## Author Biography

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.

## Table of Contents

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