2011-04-11 16:10:55 8 Comments

There's a fairly standard two or three-semester curriculum for introductory quantum field theory, which covers topics such as:

- classical field theory background
- canonical quantization, path integrals
- the Dirac field
- quantum electrodynamics
- computing $S$-matrix elements in perturbation theory, decay rates, cross sections
- renormalization at one loop
- Yang-Mills theory
- spontaneous symmetry breaking
- the Standard Model

What is a good, complete and comprehensive book that covers topics such as these?

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## 9 comments

## @AccidentalFourierTransform 2018-01-20 00:22:16

## Lecture notes.

David Tong's lecture notes. These are very basic and intuitive, and may be a good starting point for someone who has never acquainted themselves with QFT. My suggestion is to skim over these notes, and not to get hung up on the details. Once the general picture is more or less clear, the reader should move on to more advanced/precise texts.

Timo Weigand's lecture notes. I find these notes to be more precise than those of Tong, so I like them more. These notes, like those of Tong, use as main source the book by Peskin and Schröder, which I never quite liked. But Weigand, unlike Tong, has as secondary reference the book by Itzykson and Zuber, which I love. P&S aim at intuitiveness, while I&Z aim at precision; therefore, Tong may be easier/more accesible but Weigand is more correct/technical.

Sidney Coleman's lecture notes. The name of the author should be enough to make it clear that these notes are a must-read. The approach is somewhat idiosyncratic, and the text is very conversational and contains several interesting historical notes about the development of the theory, in which the author had a considerable role. Great notes to read at least once, but don't expect to learn everything there is to know there; they are meant as an introduction. Important but advanced topics are not discussed.

Jorge Crispim Romão's lecture notes. These notes are great if you are looking for a lecture-style (as opposed to textbook-style) discussion of some advanced topics. I really like these notes, because the exposition is modern, and they discuss many different topics without going into unnecessary details or becoming overly technical. The appendices are particularly useful IMHO.

Timothy J. Hollowood's lecture notes. The "Renormalization Group" part is remarkably good IMHO.

## Textbooks.

Matthew D. Schwartz, Quantum Field Theory and the Standard Model. This might be one of the best introductory textbooks out there. It is not overly technical and it covers a wide range of different topics, always from a very intuitive and modern point of view. The concepts are well motivated when introduced, and their role is usually more or less clear. This book thought me some very useful techniques that I have been using ever since.

Mark Srednicki, Quantum Field Theory. I

reallylike the organisation and design of the book, which consists of around a hundred of short and essentially self-contained chapters that introduce a single topic, discuss it in the necessary level of detail, and move on to the next topic. The discourse is linear (which is not always easy to archive), in the sense that it flows naturally from topic to topic, from easy to difficult. The only drawback of this book is that IMHO some derivations are oversimplified, and the author fails to explicitly state the omission of some technical complications. Great book nevertheless. Beware: this book is not really an introduction; it should definitely not be the first book you read. I consider it more of a reference textbook where I can check single chapters when I need to refresh some concept.Itzykson C., Zuber J.B., Quantum field theory. One of my personal favourites. The book is very precise (on the level of rigour of physics), and it contains dozens of detailed and complicated derivations that most books tend to omit. I'm not sure this book is very good as an introduction; the first few chapters are accessible but the book quickly gains momentum. Beginners may find the book slightly too demanding on a first read due to the level of detail and generality it contains. Unfortunately, it is starting to have an old feel. Not outdated, but at some points the approach is slightly obsolete by today's standards.

Weinberg S., Quantum theory of fields. As with Coleman, and even more so, the mere name of the author should be a good enough reason to read this series of books. Weinberg, one of the founding fathers of quantum field theory, presents in these books his very own way to understand the framework. His approach is

veryidiosyncratic but, IMHO, much more logical than the rest of books. Weinberg's approach is very general and rigorous (on the level of physicists), and it left me with a very satisfactory opinion on quantum field theory: despite the obvious problems with this framework, Weinberg's presentation highlights the intrinsic beauty of the theory and the inevitability of most of its ingredients. Make sure to read it at least once.Zinn-Justin J., Quantum Field theory and Critical Phenomena. This is a very long and thorough book, which contains material that cannot easily be found elsewhere. I haven't read all of it, but I

lovedsome of its chapters. His definition and characterisation of functional integrals, and his analysis of renormalisation and divergences are flawless. The philosophy of the book is great, and the level of detail and rigour is always adequate. Very good book altogether.DeWitt B.S., The global approach to quantum field theory. The perfect book is yet to be written, but if something comes close it's DeWitt's book. It is the best book I've read so far. If you want precision and generality, you can't do better than this. The book is daunting and mathematically demanding (and the notation is... ehem... terrible?), but it is certainly worth the effort. I've mentioned this book many times already, and I'll continue to do so. In a perfect world, this would be the standard QFT textbook.

Ticciati R., Quantum Field Theory for Mathematicians. In spite of its title, I'm not sure mathematicians will find this book particularly clear or useful. On the other hand, I - as a physicist - found some chapters of this book

veryuseful myself. The book is rather precise in its statements, and the author is upfront about technical difficulties and the ill-definedness (is this a word?) of the relevant objects. I very much recommend giving it a read.Scharf G., Finite quantum electrodynamics. This book will teach you that there is another way to do QFT. One that is in-between physicists' QFT and mathematicians' QFT. It is rigorous and precise, but it addresses the problems physicists care about (i.e., Feynman diagrams). In essence, the book presents the so-called causal approach to QFT, which is the only way to make computations rigorous. Spoiler: there are no divergences anywhere. This is archived by treating distributions with respect, instead of pretending that they are regular functions. The precise definition of superficial degree of divergence and momentum-space subtraction is particularly beautiful. The book left me delighted: QFT is not that bad after all.

Zeidler E., Quantum field theory, Vol. 1, 2 and 3. Initially intended to be a six-volume set, although I believe the author only got to publish the first three pieces, each of which is more than a thousand pages long! Needless to say, with that many pages the book is (painfully) slow. It will gradually walk you through each and every aspect of QFT, but it takes the author twenty pages to explain what others would explain in two paragraphs. This is a double-edged sword: if your intention is to read the whole series, you will probably find it annoyingly verbose; if, on the other hand, your intention is to review a particular topic that you wish to learn for good, you will probably find the extreme level of detail helpful. To each their own I guess, but I cannot say I love this book; I prefer more concise treatments.

## Other.

Henneaux M., Teitelboim C., Quantization of gauge systems. Not a QFT book per se, but it contains a lot of material that is essential if one wants to formulate and understand QFT properly. The presentation is very general and detailed, and the statements are very precise and rigorous. A wonderful book without a doubt.

Bogolubov, Anatoly A. Logunov, A.I. Oksak, I. Todorov, General principles of quantum field theory. A standard reference for mathematically precise treatments. It omits many topics that are important to physicists, but the ones they analyse, they do so in a perfectly rigorous and thorough manner. I believe mathematicians will like this book much more than physicists. For one thing, it will

notteach you how (most) physicists think about QFT. A lovely book nevertheless; make sure to check out the index so that you will remember what is there in case you need it some time in the future.Folland G.B., Quantum Field Theory. Similar to above, but much more approachable. The subtitle "A Tourist Guide for Mathematicians" is very descriptive. It will walk you through several important topics, but it won't in general get your hands dirty with the details.

Salmhofer M., Renormalization. An Introduction. If you care about the formalisation of Feynman diagrams and perturbation theory, I cannot recommend this book enough (or, at least, its first few chapters; I cannot really speak for the last one). It is a lovely short book.

Raymond F. Streater, Arthur S. Wightman, PCT, spin and statistics and all that. A classic text. It is short and clean, and it contains many interesting remarks.

Smirnov V., Analytic tools for Feynman integrals. A very complete collection of useful techniques that are essential to perturbative calculations, from analytic to numerical methods.

## @AccidentalFourierTransform 2018-01-20 00:22:59

I'll add some more at some point in the future. I hope this list will prove useful to some people. I will be happy to hear opinions, so make sure you leave a comment!

## @Cosmas Zachos 2018-01-20 13:36:53

Quantum Field Theoryby Lowell Brown (CUP) ISBN-13: 978-0521469463, andField Theory in Particle Physics, B de Wit and J Smith, North Holland, ISBN-13: 978-0444869999. The cognoscenti love them. One may see why.## @rbktech 2018-04-18 16:50:38

Suggestion: Add the book 'Lectures on Quantum Field Theory' by Ashok Das. I personally like it a lot

## @Permian 2018-11-24 13:47:19

@AccidentalFourierTransform what do you think of Zee's book?

## @AccidentalFourierTransform 2018-11-25 01:15:17

@Permian I've only had a very superficial look at that book, and I can't really say I'm a fan of the style. But some people do love the book, so to each their own.

## @user213887 2018-12-07 23:38:47

In addition to these, which are all great, I'd also recommend Liam Fitzpatrick's lecture notes physics.bu.edu/~fitzpatr/f16/QFTLectures.pdf

## @Mozibur Ullah 2018-01-20 02:18:33

I've got two recommendations:

QFTby Mark Srednicki. It's also available online. The presentation is clear and well-written.A Modern Introduction to QFTby Michele Maggiore. This is also very clear. It's also short which is a plus.## @Yossarian 2015-09-09 01:07:41

As somebody who has studied field theory recently for the first time I have something to say here. The one I recommend, and the one I wish it had been recommended to me is:

Quantum Field Theory and The Standard Modelby Matthew SchwartzI have to admit that I haven't gone through all of it since I have discovered it recently. But the parts I have tried are well written and the explanations are solid. It's the kind of thing you want to read for the first time

About the standard in the field, Peskin & Schroeder, I have used it to study the subject and I have disliked it a lot. True, some parts are not that bad, but overall i felt that it is sometimes too obscure. Some explanations in that book are too cryptic for the beginner in my opinion. It somehow reminded me the infamous electrodynamics Jackson book, although I still think that Peskin is a little better than Jackson.

## @pepper_chico 2016-02-22 03:35:23

I'm taking a look at this book now, and my first impression is that it's both condensed and clear.

## @Tim 2015-01-30 09:40:38

I think the didactically best book is

Student Friendly Quantum Field Theoryby Klauber.As a second book I would recommend

Gauge Theories in Particle Physicsby Aitchison and Hey or alternativelyA Modern Introduction to Quantum Fieldby Maggiore.I think Zee's QFT in a Nutshell is too dense for a beginner, but really great as a third or fourth book. The same, at least in my humble opinion, is true for the Weinberg books.

Peskin Schröder can be great to learn computations, but I find it often hard to see the bigger picture through all the computations.

## @quan 2015-01-30 09:33:05

The most complete and comprehensive approach to quantum field theory is certainly Steven Weinberg's series (Volume 1, Volume 2, Volume 3). No prior knowledge is assumed. Everything is explained from first principles. Weinberg has an amazing physical understanding and developed a major part of QFT. If you want to deepen your understanding or if you want to learn everything including important proofs these are the perfect books for you.

For beginners I recommend An Introduction to Quantum Field Theory by Peskin and Schroeder. The subject is very well-explained. As a prerequisite you should have heard about quantum mechanics. Sadly, the exercises are not the most enlightening ones.

I am aware you did not ask for lecture notes. However, these provide a more pedagogical approach. There are David Tong's lecture notes and Timo Weigand's lecture notes. Additionally, they provide exercises (partly with solutions).

## @Otto 2015-08-25 03:52:57

Prof. Eduardo Fradkin Also has some nice notes: eduardo.physics.illinois.edu/phys582

## @JohnnyMo1 2015-09-09 01:41:58

For David Tong's notes, if you want the full classroom experience, Perimeter Institute of a whole series of video lectures of him teaching what the notes cover: pirsa.org/C09033

## @Douglas Rodrigues Silva 2015-01-30 00:36:10

I studied for these books:

N.N.Bogoliubov & D.D. Shirkov, Introduction to the Theory of Quantized Fields, 3rd edition.

N.N.Bogoliubov & D.D. Shirkov, Quantum Fields, 3rd edition

They are very good, but I don't know these modern books (I believe that for a second course of quantum field theory can be good, because the Bogoliubov books are very old).

## @ali reza 2015-01-14 17:23:15

Peskin & Schroeder is really difficult and time taking books for beginning, it's exercises are not suited at all and there is least compatibility with preceding chapter. It has very bad approach to QED. And will kill all motivation to pursue. The book by Zee,

Quantum Field Theory in a Nutshell, is good for someone with background on gravity and condense matter, but will mess up the beginner's mind with bombarding of variety of topic.I personally suggest, Ashok Das, Ryder, and Mandel & Shaw. They cover whole material from Lorentz, group (Ashok Das), QED (Mandel), and path integral and renormalization (Ryder and Das).

## @Daniel Grumiller 2011-04-11 16:31:13

Anthony Zee's book QFT in a Nutshell is remarkably complete, and yet rather small. It provides a good intro to the subject.

A complete, thorough and good book is Steven Weinberg's 3-volume opus on QFT (vol. 1, vol. 2, vol. 3). It is perhaps

toocomplete for beginners.## @JamalS 2015-01-14 17:26:30

Really, Zee? It's good for a physical understanding, but I think it lacks depth.

## @Manishearth 2013-12-28 02:39:14

A list of recommendations:

^{These are recommendations from the older answers that did not follow the book policy. Plain recommendations are inappropriate now, try to explain what the book covers, it's style, etc.}