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Quantum Field Theory for the Gifted Amateur


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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

About the Author

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.


A treasury of contemporary material presented concisely and lucidly in a format that I can recommend for independent study ... I believe that this volume offers an attractive, new "rock and roll" approach, filling a large void in the spectrum of QFT books. * Johann Rafelski, CERN Courier *
The authors succeed remarkably in opening up the concepts of Quantum Field Theory to a broad, physically and mathematically trained readership. [...] The book is a valuable addition to the wide range of QFT books already available, and is suitable as self-study for the novice, as accompaniment for courses, and also as a valuable reference for those already familiar with the subject. * Physik Journal *
This is a wonderful, and much needed book ... Why have the authors been so successful? It is the way the book has been structured. Each of the 50 chapters is short. Every chapter starts with a readable plan of what is to be explained and why; and finishes with a compact summary of the key ideas that have been covered. Moreover, the language is kept as simple as possible. The aim is always to be clear and difficult ideas are approached gently. The text is interspersed with a large number of detailed worked examples which are central to the story and which are arranged so as not to intimidate the reader ... They have produced an accessible book that gives us a wonderful opportunity to understand QFT and its numerous applications * Alan D. Martin, Contemporary Physics *
There is a need for a book on Quantum Field Theory that is not directed at specialists but, rather, sets out the concepts underlying this subject for a broader scientific audience and conveys joy in their beauty. Lancaster and Blundell have written with this goal in mind, and they have succeeded admirably. * Michael Peskin, SLAC National Accelerator Laboratory, Stanford University. *
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 * Barry R. Masters, Optics & Photonics News *

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