Lecture Notes on Quantum Field Theory - Kevin Zhou

1 Lecture Notes onQuantum Field TheoryKevin Notes constitute a year-long course in Quantum Field Theory . The primary sources were: David Tong s Quantum Field Theory Lecture Notes . A clear, readable, and entertaining set ofnotes, good for a first pass through first-semester Quantum Field Theory . Timo Weigand s Quantum Field Theory Lecture Notes . Covers similar material, but from amore careful, formal point of view; it opens with LSZ reduction and handles the canonicalquantization of gauge theories in far more detail. May be too dry for a first pass, but veryuseful for clarifying points on a second pass. David Skinner s Advanced Quantum Field Theory Lecture Notes .

2 An excellent second-semesterquantum Field Theory course with differential geometry and the Wilsonian point of view bakedin throughout. Also contains a thorough list of QFT books and resources. Sidney Coleman s Quantum Field Theory Lecture Notes . A classic course from the 1980s deliveredby a legendary physicist. When I was starting out, I had a very hard time understanding themiddle third, which introduces renormalization in a rather formal way. However, the first thirdis a great introduction to the basics. Peskin and Schroeder, Quantum Field Theory . The standard book with all the standardconventions, from which many sets of Lecture Notes above draw inspiration.

3 Part I is a standard,clear introduction to the basics, though slightly sketchy when introducing interactions. Part IIcovers renormalization, using the Wilsonian point of view more than other books. Part III isexceptional, with great physical explanations and a deep exploration of practical computationsin QCD and the Standard Model at large. Srednicki, Quantum Field Theory . A newer book with a focus on the path integral. Distinguishedby its clean, modular style and nontraditional ordering of topics by spin, which allows one toencounter the conceptual novelties in interacting Field Theory , spinor representations, and gaugesymmetry separately. Has little on canonical quantization, but briefly covers topics beyond theStandard Model.

4 One downside is that it starts rather formal, and takes a long time to makecontact with familiar physics; the first third of the book covers just 3theory in six Schwartz, Quantum Field Theory and the Standard Model. A new book with a breezy, conver-sational tone. Performs many concrete calculations with modern methods, and applications tocollider physics. Has clear and fresh explanations, but also sometimes sweeps issues under therug using vague arguments or ambiguous notation (according to a reviewer: the logic can beoff-shell ). In my opinion, the main problem with this book is that it is especially sloppy in thefirst 250 pages, which is exactly where students are most likely to get confused.

5 Zee, Quantum Field Theory in a Nutshell. A fun book which focuses on the path integral andincludes applications to condensed matter. Covers a lot of ground extremely briefly. It mightnot be literally impossible to learn Quantum Field Theory by doing every calculation in the book(as Zee continuously implores the reader), but it wouldn t be an efficient route. For those withsome background already, the book is a great way to broaden knowledge. Weinberg,The Quantum Theory of Fields. A massive three-volume tome that addresses manysubtle points. The notation is dense and clunky, but this is done intentionally in the service ofmaking the logic as transparent and explicit as possible.

6 There are many natural questions onewants to ask when learning Quantum Field Theory , that all the usual books seem to completelyignore. Weinberg often has the answers; it is the book the books above refer to for the groundtruth. However, it is completely unsuitable as an introduction. Ryder, Quantum Field Theory . A friendly book which serves as a general introduction to particletheory, deemphasizing cross sections but incorporating topics like monopoles, supersymmetry,and differential geometry. It s very readable, but has little detail on the more advanced partsand no problems; best used as a supplement. Collins,Renormalization. A monograph focused on renormalization methods, which coversmany technical points skimmed over in standard books.

7 Banks,Modern Quantum Field Theory . A brief summary from a string theorist s point of view;similar spirit to Skinner s Lecture Notes . Completely useless if you don t already know quantumfield Theory ( a full pass through Peskin, Srednicki, or Schwartz), but a fun and enlighteningread if you do. The chapter on renormalization is especially good. Weinberg,Classical Solutions in Quantum Field Theory . Contains clear and insightful discus-sions of solitons, anomalies, and instantons. David Tong s Gauge Theory Lecture Notes . An absolutely exceptional set of Notes on specialtopics in Quantum Field Theory , with many references to original literature. Many insightful questions and answers on I particularly recommend the answersby Qmechanic, ACuriousMind, and Chiral to learn Quantum Field Theory can be very rough, so some people say the standard books areintentionally confusing, to make the authors look smart.

8 Nothing could be further from the a good textbook requires thousands of hours of work and years teaching with drafts of it,which implies real devotion to students. The real issue is that these books were written for capstone3courses, taken by theoretical particle physicists only, after four years of undergraduate courses andtwo years of rigorous graduate courses. They assume you ve already seen topics like relativisticclassical fields, representation Theory , Green s functions, and scattering Theory . Nowadays, manypeople want to learn Quantum Field Theory earlier, and this mismatch makes it harder to start. Beloware some student friendly ways to help bridge the gap.

9 David Tong s Quantum Field Theory Lecture Notes . Yes, again. These Notes follow the first 5chapters of Peskin and Schroeder, but with lower density, keeping about half the detail andadding double the explanation. This is a good balance for most new students. If you have astrong understanding of undergraduate physics, I think this is the best place to start. Donoghue and Sorbo,A Prelude to Quantum Field Theory . This slim new book is adaptedfrom the Lecture Notes of an undergraduate course. It clearly explains some of the trickiesttopics for beginners, including renormalization, symmetry breaking, and the interpretation ofvirtual particles, by relentlessly focusing on the simplest possible examples.

10 The book is notmeant to be comprehensive for instance, spinors are relegated to a few pages near the it is a fantastic source for supplemental reading. Greiner, Field Quantization. This crisp, clear book is used for introductory courses in roughly corresponds to the first 5 chapters of Peskin, but removes all handwaving, lays outdefinitions and rules clearly, and includes many concrete worked examples, solved at the levelof detail a beginning student would want. It can be rather dry and tiring to read, but if youprefer precision and have the time and energy, this might be the best choice. Lancaster and Blundell, Quantum Field Theory for the Gifted Amateur.