Quantum field theory is by far one of the most successful but also mysterious theories in physics. So far, there are countless popular science books on quantum mechanics on the market, but it is difficult to find one that introduces quantum field theory. A. Xu Yihong Professor Zee's recent book, Quantum Field Theory, as Simply as Possible, effectively fills this gap. The book contains the basic knowledge and concepts of quantum field theory, so that readers can understand one of the most important but confusing topics in physics in a humorous and easy-to-read article.
Quantum field theory was born out of quantum mechanics in the late 30s of the 20th century and was developed by a generation of brilliant young theorists, including Julian Schwinger and Richard Feynman. Their predictions were experimentally confirmed, and their astonishing accuracy was unmatched by other physics theories. Quantum field theory combines quantum mechanics and special relativity to provide a framework for understanding the quantum mysteries of the subatomic world.
In this book, Professor Xu Yihong, with his unique wisdom and physical insight, explains how quantum field theory can help us understand the universe and reveal some of the most profound mysteries in physics. With his easy-to-understand language, he introduces readers from diverse professional backgrounds to quantum field theory and helps them reach the frontiers of the field.
Note: Professor Xu Yihong will hold an offline readers' meeting in Shanghai in the near future to exchange with readers his recent works, including this book. Huipu will be broadcast live throughout the whole process, and relevant event information will be pushed tomorrow, so stay tuned!
*本文主体内容翻译自 Quantum Field Theory, as Simply as Possible 一书前言
徐一鸿（Anthony Zee）
Professor Xu Yihong is a well-known Chinese-American physicist, writer, and National Fellow of the United States of Sciences and Arts. He received his B.S. from Princeton University and his Ph.D. from Harvard University, and is currently a professor in the Department of Physics at the University of California, Santa Barbara.
Professor Xu Yihong's research interests are very broad, including high-energy physics, field theory, cosmology, biophysics, condensed matter physics, mathematical physics, and many other fields. In addition to academic research, his physics textbooks and popular science books are also widely known, and have been adopted by many institutions of higher learning such as Princeton University, Harvard University, Stanford University, etc., benefiting academic researchers and science enthusiasts in Europe, America and even around the world.
Preface to The Theory of Quantum Fields in the Simplest Possible
To all those who directly or indirectly taught me quantum field theory [1].
什么是量子场论(Quantum Field Theory)？
So far, there are countless popular science books on quantum mechanics on the market [2], but it is difficult to find one that introduces quantum field theory [3]. When I told an accomplished theoretical physicist that I was working on a popular science book on quantum field theory, he exclaimed, "Your book really fills in the blanks." Nowadays everyone has heard of quantum mechanics, but no one knows anything about quantum field theory. I replied, "Yes, but what's even stranger is that everyone has ever heard of string theory now." "It seems that readers of popular science books on physics have jumped directly from quantum mechanics to string theory.
In 1905, Albert Einstein pointed out that in describing particles moving close to the speed of light, we must revise the way we describe time and space on a daily basis, and unify time and space into space-time as described by special relativity. This reveals that the world of atoms and subatomic particles (e.g., electrons) is not governed by classical mechanics, but by quantum mechanics, which was also undiscovered at the time.
Take the example of an electron orbital in a hydrogen atom. While the electron in it does resemble a quantum particle, it moves quite slowly. Calculations show that the speed of an electron is less than 1% of the speed of light. Therefore, it is not necessary to intervene in special relativity [4] to study its behavior, for example, when it absorbs and radiates light. In fact, quantum mechanics is gradually assembled through the rigorous study of how atoms absorb and radiate light.
In the 19th century, Michael Faraday and James Clerk Maxwell introduced electromagnetic fields, understanding light as a form of electromagnetic waves. Electromagnetic fields travel in space at the speed of light, then, by definition, can be described by the theory of relativity. Well...... The non-relativistic electrons interact with the relativistic field.
Therefore, the basic treatment of atomic radiation light in quantum mechanics is that electrons are regarded as non-relativistic quantum dot particles, while electron-emitted light is regarded as relativistic classical fields. It was formed around 1925 and was taught to undergraduates who had no doubt about it. I told the students that this kind of half-baked treatment, even if it yielded results that were consistent with the experiment, showed a certain degree of imbalance in thinking, and it was unattractive. Theoretical physics is much more than a bunch of calculations.
Soon, and inevitably, Paul Dirac proposed in 1930 that electrons could also be described in terms of relativistic fields. Together with his colleagues, he proposed the main quantum field theory. At the same time, it was discovered that the electromagnetic field should also be governed by quantum rules, and the quanta that make up the electromagnetic field were then named photons.
In the late 40s of the 20th century, Feynman [5] and Julian Seymour Schwinger developed quantum field theory, which was later cultivated by many great scholars (you know, Feynman's main contribution to theoretical physics was quantum field theory, not quantum mechanics, as is often said on the Internet). As one of my professors once said, quantum field theory was reborn in the 70s of the 20th century with a parade of victory that filled the audience with wonder and joy.
In short, quantum field theory arises from the combination of quantum mechanics and special relativity. It is also the most accurately tested theory in physics, far surpassing Newtonian mechanics and quantum mechanics.
The birth of this book
Twenty years ago, I wrote a textbook on quantum field theory, followed by a textbook on Einstein's gravity. I would like to talk first about the most wonderful subject of theoretical physics in my eyes, and then the second wonderful [6]. Once, I was chatting with Ingrid Gnerlich, editor at Princeton University Press, about the possibility of writing two more accessible books to complement the first two textbooks. So, in 2016 I signed a contract for two more books.
I started with an easier path. Despite such topics as space-time bending, Einstein's gravitational force is still more solid and understandable than quantum field theory. As a result, On Gravity was published in 2018 (see image below). But I still put off writing the popular science book on quantum field theory and started writing Fly by Night Physics, which was published in 2020. I subconsciously thought that popular science about quantum field theory would be very difficult to write.
Pictured: So far, On Gravity has been translated into Chinese, Czech, Turkish, Italian and Spanish. The Spanish publisher also translated the cover design! Note that a "la" was added to the title, but it was omitted from the design. In addition, "Gravedad" did not fall all the way to the bottom, but was held up by an unknown force.
The reason for this is obvious. Even a brief introduction to quantum field theory would have to go through special relativity and quantum mechanics, but I can't expect the reader to already know about it beforehand. Therefore, the first two parts of the book are devoted to a brief introduction to them, the two pillars of twentieth-century physics. I have to be extremely concise, unless you want to have a thousand-page book in your hand. As much as I would love to introduce the wonderful and fascinating quantum field theory to as many readers as possible, the reality is that readers who have never heard of special relativity and quantum mechanics are unlikely to read this book. In addition, the other extreme of the readership should be able to read these two introductory chapters quickly.
Before the first two parts, I wrote an introduction to quantum field theory, outlining a roadmap for our exploration. This section is intended to provide an overview, not an introduction to the full details of quantum field theory. So, even if you can't understand some of the words in the introduction, you don't have to be nervous.
Since the publication of my textbook on quantum field theory in 2003, I have lectured extensively around the world [7]. When I spoke to my editor, Ingrid, I was a little naïve to turn the slides of my talk into a book. But I realized right away that in order for the slideshow to look organized, I had to add a lot of connections and explanatory parts. However, you may notice that some of the charts in this book are still presented in the form of slides.
Who this book is addressed to: The Two Ends of the Spectrum
For the young, but also for the elderly, yes, both.
I'd love to reach the next generation of theoretical physicists, bright college students, and even high school students who want to major in physics. I put some "bait" in the book to attract them. These are mostly written in endnotes. Some of the chapters in Part V were also written for this particular group.
I sometimes think about myself when I was younger. In the summer of my junior year, a professor asked me to read a huge book on quantum field theory, probably one of the worst textbooks written in any field of physics. The book I write now will be of great help to me back then when I was struggling painfully in the humid weather of central New Jersey because it showed the reader the entire forest rather than the individual trees [8]. (The funny thing about this story is that the professor asked me to re-read the book from the first page when he came back in the fall.) I sometimes ask my students to do that. In fact, it's a good piece of advice: read the same book twice. ）
Judging from the emails I receive, most of the readers of my popular science books are scientists, engineers, doctors, lawyers, and other professionals, many of whom are retired and some of whom are not. Quite a few people were brave enough to read the textbook I had written. I applaud these older readers and salute them as I write.
Young or old, or anyone else, don't be intimidated. The mysteries of the quantum are mysterious and difficult to understand in the language of everyday experience. If you come across something you don't understand, just skip it. If you don't understand a concept, just because I don't have the place to describe it in detail, sometimes you can't find the right language. This book is intended to give the reader a taste of quantum field theory, not to make it proficient. When I was writing popular science books on physics, I used to send manuscripts to friends who weren't physicists. A friend who has read a lot of popular science books compares them to fast food. Still, he said the book was like a more nutritious, hearty meal, and the more elaborate dishes awaited him in the textbook.
Princeton University Press regularly sends manuscripts of books to professional readers for review. One reader wrote, "This book offers a unique perspective that no other book has, and accordingly, it has high expectations from readers." So this is not your average popular science book...... The point is that Zee is pushing for what popular science books can do as much as possible. Quantum field theory is not an easy subject to describe to the layman, which forced Zee to finish the book at a higher level. "That's right! This reader knows exactly what I want to do.
When I need to satisfy readers of all the different classifications, I especially want to appeal to young people, who are the physicists of the future. With them in mind, I've added some additional mathematical expressions and proofs to the endnotes [9]. Needless to say, I would be very happy if some college students, and even some high school students, could be inspired by this book and go on to read a textbook on quantum field theory.
I dare say that this book will be helpful even for readers who have already decided to enter the field of theoretical physics. A friend who received my manuscript wrote: "This book will be an excellent read before I studied James D. Bjorken and Sidney D. Drell's Relativistic Quantum Field [10] at Caltech in 1984. ”
I sat down with Rob Phillips, a distinguished physics professor at Caltech, about the value of writing popular science books and textbooks. He used himself as an example [11] to illustrate that a popular science book has the potential to completely change the trajectory of young people's lives. He was absolutely right. Textbooks are for those who have already decided that they want to study physics.
The vision of the book
I don't like cramming my popular science books with the latest and hottest content. You can find these online, but "caveat emptor". I prefer to write something old and cold, that is, something more complete and cherished. Yes, I know that some people like bold doctrines, and the more confusing the connection between those boundless imaginations and reality, the better. But it's the kind of stuff that even physicists quickly forget, or prefer not to know in the first place. In this book, we will stay in the only universe that we know and love. To be clear, this is not a book on string theory, it is a questionable theory that will most likely be revised in the future; This is a book on quantum field theory, a well-established theory that has existed in some form for almost a hundred years.
As readers of my other books know, I like to insert all sorts of interrelated anecdotes into the endnotes. Readers often write to me that these endnotes are not only informative, but sometimes very entertaining. On the other hand, some readers may find them distracting. If that's the case, just ignore the endnotes and come back to read them later. Everyone has their own preferences!
How much math do you need to know to read this book
It is difficult for those who do not understand mathematics to feel the most profound beauty of nature...... If you want to understand and appreciate nature, you have to understand the language she speaks. —R.P. Feynman
I couldn't have spoken better than "that man" or been more authoritative than he was. Analogies abound in trying to appreciate theoretical physics without mathematics: reading an article about a piece of music without listening to it, watching a serious foreign film without subtitles. Here's my version of the metaphor: Imagine yourself blindfolded and wearing thick winter gloves trying to appreciate the beauty of blooming flowers.
A few years ago, I wrote the preface to Feynman's classic book on quantum electrodynamics [12]. As I read that book, I kept muttering, "Oh, Feynman, if you write the formula in this place, everything will be very clear." But he was certainly not allowed to do so. (Refers to a series of lectures Feynman gave to an audience with no scientific training in his later years, later compiled into QED: The Strange Theory of Light and Matter, published by Princeton University Press, with less use of formulas and mathematical discourse.) Me too. But I dare to rebel and break the rules in this book.
If you flip through the book, you will see some mathematical symbols and even some equations here and there. Take it easy! You are not eligible, let alone assigned, to take the final exam in quantum field theory.
In many cases, mathematics is merely a concise symbol in place of complicated text. And it's usually just standard mathematical terms. Do you want me to keep saying "variation in space" instead of "space derivatives"? Similarly, in the chapter on Dirac-Feynman path integrals, I started by saying "a wonderful sum", but eventually gave up and wrote "integrals" and mathematical symbolic ∫. Because that's what Dirac and Feynman were talking about, integrals, not "wonderful sums"! Obviously, you are not being asked to integrate something, and you can continue to think of integrals as "wonderful sums" if you want. But from what I've seen of both types of readers, I'm sure young and old know some calculus (don't worry about what counts as "knowing"). I have also provided a table of mathematical notation and notation, which may help some readers.
As another example, it is almost impossible to seriously discuss quantum mechanics without complex numbers: it has been expressed in complex numbers since day one. It's like a biology book without the words "cell" or "DNA," or an accounting book without numbers. Here's a free piece of advice: Be wary of any popular science book on quantum mechanics that doesn't mention complex numbers.
In several of my books, I quote Albert Einstein's dictum: "Physics should be as simple as possible, but it can't be simpler." The same goes for this book, I tried to keep a rather esoteric subject as simple as possible, but I also realized that if I made it too simple, the book might become a tedious generalization like some popular physics books on the market (excluding the table of contents that are deliberately compiled into shocking facts). Still, it should be clear to the discerning reader that if I explain it in more detail, the book could easily become ten times thicker than it is now.
The choice of topic
Quantum field theory is an extremely informative topic, so I had to omit many interesting topics and briefly address the ones I covered. Although quantum field theory has been widely used in various fields of physics (especially condensed matter theory) over the past few decades, it has developed from particle theory and has achieved its most brilliant achievements there. Therefore, in the fifth part, I am obliged to introduce the basic interactions, including the strong, weak, and electroweak interactions, the grand unified theory, and gravity, and I limit myself to one section each. (One reader said he wanted to learn more about particle physics, but the book was about quantum field theory, not particle theory.) Finally, at the urging of another reader, a long chapter on Einstein's gravity was split in two: classical and quantum. Obviously, it doesn't make sense to cram all this material into just a few chapters, but I don't have a choice.
On the other hand, I had planned to devote a separate chapter to spin and statistics, which would be enough for five or six pages. I could have stopped there, but then I realized that just saying something like "you can't tell who's who in a quantum world" would only make the book more difficult to understand than I thought [13]. So I've spent a lot of space on this topic, which I think is central to our understanding of the physical world, and I've expanded that material into Part VI.
Here's a preview of the conclusion of a wonderful chapter: I dedicate a chapter (Part 5, Chapter 1) to the crowning achievement of relativistic quantum physics, the existence of antimatter. This argument is unbelievably simple and beautiful!
Positioning of the book
According to the traditional understanding, this book is positioned between textbooks and popular science books. However, this book is still a popular science book, probably a little more specialized than most popular science books, and is intended to provide an overview. So I'm going to have to skim over some technical details here and there, or something that's not entirely accurate. A hint to the nitpickers: I know what I'm talking about. For example, I know the difference between invariance and covariance, the difference between gauge field and gauge potential, and so on. After all, I wrote a textbook on quantum field theory. But if I were to switch back and forth, always using the right vocabulary, it would only confuse most readers.
There are several possible types of popular science books on physics. A more descriptive type is one that focuses on processes and phenomena, such as this nucleon colliding with that nucleon, a star dying and exploding. The other is full of bold imagination, talking about the beginning of time (or more genius talking about what happened before time appeared, *smile*), multidimensional universes, and so on. These kinds of books are easy to read, but they come at a cost: they don't provide deep understanding. In this book, I have chosen to emphasize the conceptual foundations, which are the key to making quantum field theory quantum field theory -- in other words, the hard parts. But I can also feel the frustration of some readers [14]. Allow me to give you some advice. You can read ten popular science books, but you understand less than you can read a textbook on quantum field theory. If you have the necessary expertise to understand textbooks, be sure to read them. Even the painstaking reading of a few introductory chapters is worth it.
Disclaimer about real history
Finally the disclaimer arrived. This is not an academic paper, but a popular science book intended to provide an overview of quantum field theory. Between historical accuracy and the vividness of the narrative, I chose the latter more. No, Paul Dirac didn't realize the existence of antimatter in a flash of inspiration. But if I were to mention all the people who helped him think of this, the book would be going to be very thick. No, Werner Heisenberg did not propose the isospin as we know it, but rather the exchange of protons and neutrons. History is intricate. Unfortunately and unpleasantly, writers of popular science books on physics have had to promote the Matthew effect[15] and create myths about a few great figures who made major contributions to the progress of physics. I've added some historical material to the endnotes.
Thanks
我感谢那些对稿件的各个部分提出意见的人: Linda Robbins Coleman, Joshua Feinberg, Andrew Greenwood, John Hart, Greg Huber, Brian Kent, Nadie LiTenn, Lewis Robinson, Richard Scalettar, Steve Weinberg, Mark Weitzman, Andrew Zee, 和 Peter Zee。 （这个小组包括一名律师、一名古典音乐作曲家和指挥家及音乐会钢琴演奏家、一名生物物理学家、一名神经学家、 一名澳大利亚联邦法院法官、一名进化生物学家、一名计算机科学家、一名退休的职业扑克玩家、三名物理学家和两名本科物理专业的学生。 )
At Princeton University Press, my editor, Ingrid Gnerlich, has been enthusiastic and supportive of the book from the very beginning. She again commissioned my long-time collaborator, Cyd Westmoreland, to proofread and hand over the actual production to Karen Carter. I also thank Christie Henry, president of Princeton University Press, for her vision and humor. The help of Craig Kunimoto, Alina Gutierrez and David Reiss with computers was indispensable. As always, I enjoyed Janice and Max's company and encouragement.
exegesis
[1] 直接影响来自课程培训和面对面指导，感谢 Sidney Coleman, Julian Schwinger, ArthurWightman, Sam Treiman，以及 James Hartle 等。 间接影响来自教科书和畅销书，感谢 SteveWeinberg, Richard Feynman, John Jun Sakurai, James Bjorken 和其他许多人。
[2] Some of these books tend to emphasize the stranger aspects, but that's not what I wanted.
[3] 在某种程度上，我的书《可畏的对称》（Fearful Symmetry: The Search for Beauty in Modern Physics）涉及量子场理论的一些方面。
[4] For the innermost electrons of heavy elements, such as uranium, its correction in the case of special relativity cannot be ignored.
[5] The reader who holds the book now is likely to be an admirer of Feynman, and so am I; But I don't worship him as a supreme god, as many do.
[6] Later, I wrote a textbook on group theory, which for me was the third most interesting subject in theoretical physics.
[7] More recent examples have included Bangladesh, China, India, Sweden and Brazil, as well as the University of Cambridge in the United Kingdom.
[8] By the way, I am now convinced that the author of the book on quantum field theory I read did not even see the forest; He may have tripped over a piece of wood and hit his head. In fact, he showed me the bark of a tree, not a tree.
[9] For example, in Chapter I.3, I dared to add the derivation of the trigonometric functions of hyperbola.
[10] Bjorken and Drell's Relativistic Quantum Fields is a well-known textbook from which I also learned. Note that Jim Bjorken is also mentioned in endnote 1 and is known as "Bj" in my circle.
[11] Instead of college, Rob worked as an electrician, read books (including popular physics books), and was eventually accepted into an elite graduate school.
[12] R. P. Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press, 2014.
[13] Some readers may complain that this is incomprehensible. And the more sophisticated person will realize that the best I can do in a popular book is to give you an overview of the topic. Of course, I invite you to continue reading textbooks on quantum field theory, including my "Quantumn Field Theory in a Nutshell: Second Edition."
[14] Several people on Amazon thought some of my books were too difficult, while others complained that they were too easy. Well, it's simple: if you want to learn a little less, go for a popular hit book like Fearful Symmetry: The Search for Beauty in Modern Physics, and if you want to learn a little more, read QFT Nut (Quantum Field Theory in a Fruit Shell).
[15] R. Merton, sociologist The Matthew principle proposed by K. Merton has been fully exploited in theoretical physics. For some examples of gravity, see the footnote on page 169, the endnote on page 376, etc. in G Nut.
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