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.

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Table of Contents

Part I The Universe as a set of harmonic oscillators
Chapter 1 Lagrangians
Chapter 2 Simple Harmonic Oscillators
Chapter 3 Occupation Number Representation
Chapter 4 Making Second Quantization Work

Part II Writing down Lagrangians
Chapter 5 Continuous Systems
Chapter 6 A First Stab At Relativistic Quantum Mechanics
Chapter 7 Examples Of Lagrangians, Or How To Write Down A Theory

Part III The need for quantum fields
Chapter 8 The Passage Of Time
Chapter 9 Quantum Mechanical Transformations
Chapter 10 Symmetry
Chapter 11 Canonical Quantization Of Fields
Chapter 12 Examples Of Canonical Quantization
Chapter 13 Fields With Many Components And Massive Electromagnetism
Chapter 14 Gauge Fields And Gauge Theory
Chapter 15 Discrete Transformations

Part IV Propagators and perturbations
Chapter 16 Propagators And Green’S Functions
Chapter 17 Propagators And Fields
Chapter 18 The S-Matrix
Chapter 19 Expanding The S-Matrix: Feynman Diagrams
Chapter 20 Scattering Theory

Part V Interlude: wisdom from statistical physics
Chapter 21 Statistical Physics: A Crash Course
Chapter 22 The Generating Functional For Fields

Part VI Path integrals
Chapter 23 Path Integrals: I Said To Him, ‘You’Re Crazy’
Chapter 24 Field Integrals
Chapter 25 Statistical Field Theory
Chapter 26 Broken Symmetry
Chapter 27 Coherent States
Chapter 28 Grassmann Numbers: Coherent States And The Path Integral For Fermions

Part VII Topological ideas
Chapter 29 Topological Objects
Chapter 30 Topological Field Theory

Part VIII Renormalization: taming the infinite
Chapter 31 Renormalization, Quasiparticles And The Fermi Surface
Chapter 32 Renormalization: The Problem And Its Solution
Chapter 33 Renormalization In Action: Propagators And Feynman Diagrams
Chapter 34 The Renormalization Group
Chapter 35 Ferromagnetism: A Renormalization Group Tutorial

Part IX Putting a spin on QFT
Chapter 36 The Dirac Equation
Chapter 37 How To Transform A Spinor
Chapter 38 The Quantum Dirac Field
Chapter 39 A Rough Guide To Quantum Electrodynamics
Chapter 40 Qed Scattering: Three Famous Cross-Sections
Chapter 41 The Renormalization Of Qed And Two Great Results

Part X Some applications from the world of condensed matter
Chapter 42 Superfluids
Chapter 43 The Many-Body Problem And The Metal
Chapter 44 Superconductors
Chapter 45 The Fractional Quantum Hall Fluid

Part XI Some applications from the world of particle physics
Chapter 46 Non-Abelian Gauge Theory
Chapter 47 The Weinberg–Salam Model
Chapter 48 Majorana Fermions
Chapter 49 Magnetic Monopoles
Chapter 50 Instantons, Tunnelling And The End Of The World

Appendix A Further Reading
Appendix B Useful Complex Analysis