Quantum Field Theory for the Gifted Amateur

Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in detail. Using numerous worked examples, diagrams, and careful physically motivated explanations, this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that quantum field theory provides, and which all physicists should have the opportunity to experience.

Table of Contents

Part I The Universe as a set of harmonic oscillators

1 Lagrangians

2 Simple harmonic oscillators

3 Occupation number representation

4 Making second quantization work

Part II Writing down Lagrangians

5 Continuous systems

6 A first stab at relat ivistic quantum mechanics

7 Examples of Lagrangians, or how to write down a theory

Part Ill 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 electromagnet ism

14 Gauge fields and gauge theory

15 Discrete transformations

Part IV Propagators and perturbations

16 Propagators and Green’s functions

17 Propagators and fields

18 The S-matrix

19 Expanding the S-matrix: Feynman diagrams

20 Scattering theory

Part V Interlude: wisdom from statistical physics

21 Statistical physics: a crash course

22 The generating functional for fields

Part 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

Part VII Topological ideas

29 Topological objects

30 Topological field theory

Part 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

Part 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

Part 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

Part 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 lnstantons, tunnelling and the end of the world

About the Authors

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.