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.

This wonderful and exciting book is optimal for physics graduate students. The authors are brilliant educators who use worked examples, diagrams and mathematical hints placed in the margins to perfect their pedagogy and explain quantum field theory

Autorentext

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.

Klappentext

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.

Inhalt

• 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