The first time I talked about quantum field theory, I was a professor of nuclear physics, and the main textbook I used was

Greiner's Relativistic Quantum Mechanics+Field Quantization+Quantum Electrodynamics

A Brief Introduction to Peskin's Quantum Field Theory

Greiner wrote it in detail, which I think is both an advantage and a disadvantage.

The advantage is that every time you look at the ambiguity on Peskin, you can look at Greiner, who usually has some explanations.

The disadvantage is that I don't think such a detailed book is suitable for self-study. First of all, the book is not attractive, and there are so many details, so in the struggle between perseverance and time, I believe that few people can persist until the end.

Another feature of Greiner's book is that his set of books is a complete system, which is obviously an advantage and a disadvantage.

Especially when you are reading a book, you will always quote the conclusions of several other books from time to time.

Peskin's book My feeling is that this book is suitable for a teacher who has carefully studied this book and has his own understanding of the framework of field theory to lead students to learn, but generally not suitable for self-study.

Greiner and Peskin's book system has a * * similarity, that is, scalar field, spinor field and vector field are quantized together, which is convenient for us to see the difference of field quantization with different spins.

But there are so many bags on the backpack that it is difficult to reach the distance. There are many necessary mathematical skills and details in quantum field theory, such as gamma matrix of spinor field and standardization of vector field. But we can easily get lost in these details and lose sight of the overall framework of field theory.

Later, I took a class on quantum field theory, which was taught by a senior professor of particle physics.

The textbook used is Srednicki's quantum field theory.

The teacher divided the course of quantum field theory into I and II and taught it for one academic year.

In the first semester, I only talked about the spin-0 part in Srednicki's book, that is, I only talked about scalar fields.

In the second semester, I talked about spin- 1/2 and spin- 1 in Srednicki's book, that is, spinor field and vector field.

The characteristics of this book are obvious, and Srednicki pays more attention to the establishment of field theory framework.

Scalar field has no rich internal structure (spin, gauge), so we can pay full attention to the structure of field theory by explaining scalar field.

Quantization of field, asymptotic expansion, Feynman diagram, renormalization (group), spontaneous symmetry breaking.

All these can be clearly displayed in the framework of scalar field. Next, when it comes to spinor field and vector field, we still use the same framework, but slowly add the internal structure, such as dealing with spin, introducing Lorenz group and gamma matrix, dealing with norm, introducing group representation theory and so on.

Of course, I think this statement and Peskin's statement are complementary, which can make us notice the different structures of the theory of presence.

After all, the structure of field theory cannot be simply and rudely distinguished according to spin.

First of all, I think Srednicki's book is very suitable for self-study, because if you can finish the first part before the passion dies, I think it is enough for you to appreciate the structure of the theory of presence. Compared with Peskin, Srednicki simply tells you the details by hand. But to be honest, this book gives me the feeling that it makes sense for me to read Griffith when I was studying quantum mechanics, but in fact it's a bit evasive, and many details can't be brushed aside like in the book.

At this time, Weinberg's three-volume quantum field theory has to be mentioned.

I guess some field theorists can learn quantum field theory directly by studying these three books, such as Xu C.K. or Qi X.L.

Anyway, I can always find reasonable arguments from Weinberg every time I hide in Slade Nicky, but for a person who does condensed matter theory like me, finishing these three books is a bit like a drop in the ocean.

Besides, I haven't read A.Zee's book, so I won't comment for the time being.

There are two kinds of formalism in general field theory.

Canonical form and path integral form.

The establishment of early field theory is generally based on normative formalism.

This is well understood in condensed state field theory, because secondary quantization is the natural representation of multi-particle system, and many structures of field theory are directly included in the reciprocal relationship of operators.

There are three books based on normative formalism.

The first book is the quantum field theory method in statistical physics of Landau School of the Soviet Union, commonly known as AGD.

The classics of this book become more and more obvious with time, especially with the study of unconventional superconductivity. Although the pairing mechanism cannot be explained by electro-acoustic coupling, the field theory description of superconducting copper pairs can still be put into the original framework. My undergraduate thesis is based on this book and AGD's paper in 1960s to deal with the impurity effect in unconventional superconductivity.

The second book is "Quantum Theory of Multi-particle Physics" by American Fett.

To some extent, AGD is short and pithy, and it needs its own brain to fabricate a lot of calculation details. Feitl's book, on the other hand, is different. Just the second quantization, he has a whole chapter. If you want to have a deeper understanding of secondary quantization and don't want to read those monographs half a century ago, I personally think this chapter is the essence of secondary quantization in that era.

This book was written with a professor of nuclear physics. I don't know anything about nuclear physics, but when there are many hadrons in the nucleus and the speed is not so fast, it becomes a non-relativistic multi-body problem, which can be placed in the same framework as the solids studied in condensed matter.

So I think this book is very suitable for self-study, but it needs enough perseverance. After all, it is not as thin as AGD.

The third book is Mahan's multi-particle physics.

This book is a book with obvious pragmatic characteristics. It tells you how to use secondary quantization, how to use wick theorem and Feynman's law, but he can't tell you why. If you are the kind of person who likes to get to the bottom of things, then this book will make people very uncomfortable. But if you want to learn how to do it in a short time, then this book is very suitable for you. Compared with the first two books, the only advantage of this book is that it was published late, so it contains some relatively new contents, such as some strong correlation models, such as quantum Hall effect. My personal view of this book is just like Zeng's Quantum Mechanics. Don't take the time to watch it if it's okay. If you have any questions, you can turn them over, which may help. After all, it is just a reference book, and there is not much physics.

If we only deal with some minor problems, both canonical formalism and path integral formalism are actually enough. Which one are you familiar with, western or clam?

However, with the emergence of quantum Hall effect and high temperature superconductivity, condensed matter began to pay attention to the strong correlation problem, and the traditional perturbation theory failed here.

Some new methods have appeared, such as static phase approximation, renormalization group and so on. These methods can be clearly shown in path integral formalism, and accordingly, many monographs have begun to restate the theory of condensed state field with path integral formalism.

Let me talk about some books I have read here.

The first book, Wen Xiaogang's quantum many-body theory.

Similar to Srednicki's classification of fields according to spins, Wen Xiaogang's previous chapters classified fields according to bosons and fermions. Mathematically, bosons can be described by complex numbers, and fermions can be described by Glassman numbers. But there are gains and losses in any classification, and many very important structures, such as Green's function and renormalization group, become a calculation detail here.

Wen Xiaogang's excellent book is devoted to explaining the lattice gauge theory in a chapter, which is completely absent in early textbooks, but it is a very important part of understanding the strong correlation problem.

But to tell the truth, Wen Xiaogang's book is called Xiao Yao, and his thoughts are complicated, and he brought a lot of bootleg goods. Beginners should not be too involved. But if you have a certain foundation of condensed matter field theory, this book will certainly give you a lot of inspiration.

I think people in Tsinghua usually play this book fluently.

Second, Nagaosa's two books on quantum field theory in condensed matter/strong correlation.

Perhaps it is because Nagaosa started with quantum mechanics that undergraduates are familiar with. Many people think this book looks easy, but only if you don't read the third chapter and beyond.

In my opinion, Nagaosa describes the most basic and important concepts in condensed matter field theory with the most appropriate examples and the least pen and ink. If you use this book to learn condensed matter field theory for the first time, it will be more difficult to start from the third chapter.

Because Nagaosa cherishes ink as gold, scalar field, vector field and gauge field must be quantized together, and many details are obviously insufficient, so I think this book is more suitable for a systematic review after learning condensed matter field theory once.

The third book, Introduction to Classical and Quantum Field Theory, by Wu Taikai.

The preface of this book shows that this book is written to introduce the above two books.

Personally, I think this book is really suitable for getting started, but since the author is my boss's boss, it is also an advertisement.

The fourth book, autran &; Simmons' theory of condensed matter field

This book is very suitable for self-study, because considering the arrangement of this book, I can hardly imagine anyone using it as a teaching material, but self-study needs a correct way to open it.

To tell the truth, I think every chapter of this book is illogical and messy, but when it organizes these contents in a certain order, suddenly that feeling comes, maybe this is also the charm of condensed state.

This book is not detailed, and you have to make up many calculation details yourself, but the characteristic of this book is that you can get as much from it as you spend.

This book is divided into two chapters on renormalization groups and topology. I think it is the essence of this book, which must not be missed.

Although reorganization is not as good as Shankar's, topology is certainly not as detailed as なかはら まこと's.

The second edition of this book adds the non-equilibrium state field theory. I haven't done the relevant topic yet, so I won't comment for the time being.

The only drawback is that there is no chapter on lattice gauge field theory in this book, which may be related to the author's research field

The fifth book, Negele &；; Orland's Quantum Multiparticle System

As a member of ABC series, I don't need to say more about the status of this book.

I believe it takes a lot of perseverance to finish reading this book. It may take you an hour to realize that you have read a piece of paper.

But of course, the details of this book are complete and the framework is clear, so the rest are all readers' problems.

Another feature of this book is that many of its essences actually appear in the form of exercises, so if you haven't done exercises, it's almost as if you haven't read this book.

The only regret is that as a classic work like AGD, this book does not have much recent content, such as quantum Hall effect, which can be used for reference by Altland &；; Simmons' book to supplement, from the perspective of advancing with the times, Ortland &; Simmons did a good job.

Finally, a little yellow book, Interaction Electrons and Quantum Magnetism by auerbach.

The appendix of this book is a simplified version of the condensed matter field theory of path integral formalism.

This book mainly takes the quantum Heisenberg model as an example to show the framework of condensed matter field theory.

If the mathematics behind quantum mechanics is linear algebra,

Then the course of quantum field theory is essentially an algebra study.

Algebra not only tells us a set of calculation rules, but also tells us the structure/framework of the object.

The algebraic structure behind quantum field theory is very rich and complex, and we may just catch a glimpse of the tip of the iceberg.

PS: Finally, I introduced several books on condensed matter field theory in a hurry, so I won't have time to add them next time. However, if I encounter the right problem, I think I will still talk about my superficial understanding of other problems.