Quantum field theory provides the theoretical backbone to most modern physics. This book is designed to bring quantum field theory to a wider audience of physicists. It is packed with worked examples, witty diagrams, and applications intended to introduce a new audience to this revolutionary theory.

• 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

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.