量子场论(英文版)

　　在现代物理学中，量子场论是功能异常强大，用途极其广泛的理论工具。它的特点是通过大量的数学计算定量地刻画物理现象。本书详细介绍量子场论方法，读者只需要掌握了基本的量子力学和狭义相对论知识就能读懂。作者从简单事例引出现象背后的深刻物理概念，利于理解；从不同历史时期的经典成果讲到现代议题，便于掌握。全书层次分明，循序渐进。内容编排做了模块化处理，每章自成系统，对必要的预备知识都做了详细的说明，读者可以根据自己的兴趣研读相关的章节。本书对于理论物理和粒子物理专业的研究生，是非常理想的教材，对于其它相关领域的研究人员也是非常好的参考读物。
　　 读者对象：理论物理、凝聚态物理和场论等专业的高年级本科生、研究生和相关专业的科研人员。

preface for students
preface for instructors
acknowledgments
part i spin zero
1 attempts at relativistic quantum mechanics
2 lorentz invariance (prerequisite: 1)
3 canonical quantization of scalar fields (2)
4 the spin-statistics theorem (3)
5 the lsz reduction formula (3)
6 path integrals in quantum mechanics
7 the path integral for the harmonic oscillator (6)
8 the path integral for free field theory (3, 7)
9 the path integral for interacting field theory (8)
10 scattering amplitudes and the feynman rules (5, 9)
11 cross sections and decay rates (10)
12 dimensional analysis with h = c = i (3)
13 the lehmann-kallen form of the exact propagator (9)
14 loop corrections to the propagator (10, 12, 13)
15 the one-loop correction in lehmann-kallen form (14)
16 loop corrections to the vertex (14)

　　Quantum field theory is the basic mathematical language that is used to describe and analyze the physics of elementary particles. The goal of this book is to provide a concise, step-by-step introduction to this subject, one that covers all the key concepts that are needed to understand the Standard Model of elementary particles, and some of its proposed extensions.
　　In order to be prepared to undertake the study of quantum field theory, you should recognize and understand the following equations:
　　This list is not, of course, complete; but if you are familiar with these equations, you probably know enough about quantum mechanics, classical mechanics, special relativity, and electromagnetism to tackle the material in this book.
　　Quantum field theory has the reputation of being a subject that is hard to learn. The problem, I think, is not so much that its basic ingredients are unusually difficult to master (indeed, the conceptual shift needed to go from quantum mechanics to quantum field theory is not nearly as severe as the one needed to go from classical mechanics to quantum mechanics), but rather that there are a lot of these ingredients. Some are fundamental, but many are just technical aspects of an unfamiliar form of perturbation theory.
　　In this book, I have tried to make the subject as accessible to beginners as possible. There are three main aspects to my approach.
　　Logical development of the basic concepts. This is, of course, very different from the historical development of quantum field theory, which, like the historical development of most worthwhile subjects, was filled with inspired guesses and brilliant extrapolations of sometimes fuzzy ideas, as well as its fair share of mistakes, misconceptions, and dead ends. None of that is in this book. From this book, you will (I hope) get the impression that the whole subject is effortlessly clear and obvious, with one step following the next like sunshine after refreshing rain.
　　Illustration of the basic concepts with the simplest examples. In most fields of human endeavor, newcomers are not expected to do the most demanding tasks right away. It takes time, dedication, and lots of practice to work up to what the accomplished masters are doing. There is no reason to expect quantum field theory to be any different in this regard. Therefore, we will start off by analyzing quantum field theories that are not immediately applicable to the real world of electrons, photons, protons, etc., but that will allow us to gain familiarity with the tools we will need, and to practice using them. Then, when we do work up to "real physics," we will be fully ready for the task. To this end, the book is divided into three parts: Spin Zero, Spin One Half, and Spin One. The technical complexities associated with a particular type of particle increase with its spin. We will therefore first learn all we can about spinless particles before moving on to the more difficult (and more interesting) nonzero spins. Once we get to them, we will do a good variety of calculations in (and beyond) the Standard Model of elementary particles.
　　User friendliness. Each of the three parts is divided into numerous sections. Each section is intended to treat one idea or concept or calculation, and each is written to be as self-contained as possible. For example, when an equation from an earlier section is needed, I usually just repeat it, rather than ask you to leaf back and find it (a reader's task that I've always found annoying). Furthermore, each section is labeled with its immediate prerequisites, so you can tell exactly what you need to have learned in order to proceed. This allows you to construct chains to whatever material may interest you, and to get there as quickly as possible.
　　That said, I expect that most readers of this book will encounter it as the textbook in a course on quantum field theory. In that case, of course, your reading will be guided by your professor, who I hope will find the above features useful. If, however, you axe reading this book on your own, I have two pieces of advice.
　　The first (and most important) is this: find someone else to read it with you. I promise that it will be far more fun and rewarding that way; talking about a subject to another human being will inevitably improve the depth of your understanding. And you will have someone to work with you on the problems. (As with all physics texts, the problems are a key ingredient. I will not belabor this point, because if you have gotten this far in physics, you already know it well.)
　　The second piece of advice echoes the novelist and Nobel laureate William Faulkner. An interviewer asked, "Mr. Faulkner, some of your readers claim they still cannot understand your work after reading it two or three times. What approach would you advise them to adopt?" Faulkner replied, "Read it a fourth time."
　　That's my advice here as well. After the fourth attempt, though, you should consider trying something else. This is, after all, not the only book that has ever been written on the subject. You may find that a different approach (or even the same approach explained in different words) breaks the logjam in your thinking. There are a number of excellent books that you could consult, some of which are listed in the Bibliography. I have also listed particular books that I think could be helpful on specific topics in Reference Notes at the end of some of the sections.
　　This textbook (like all finite textbooks) has a number of deficiencies. One of these is a rather low level of mathematical rigor. This is partly endemic to the subject; rigorous proofs in quantum field theory are relatively rare, and do not appear in the overwhelming majority of research papers. Even some of the most basic notions lack proof; for example, currently you can get a million dollars from the Clay Mathematics Institute simply for proving that nonabelian gauge theory actually exists and has a unique ground state. Given this general situation, and since this is an introductory book, the proofs that we do have are only outlined.
　　Another deficiency of this book is that there is no discussion of the application of quantum field theory to condensed matter physics, where it also plays an important role. This connection has been important in the historical development of the subject, and is especially useful if you already know a lot of advanced statistical mechanics. I do not want this to be a prerequisite, however, and so I have chosen to keep the focus on applications within elementary particle physics.
　　Yet another deficiency is that there are no references to the original literature. In this regard, I am following a standard trend: as the foundations of a branch of science retreat into history, textbooks become more and more synthetic and reductionist. For example, it is now rare to see a new textbook on quantum mechanics that refers to the original papers by the famous founders of the subject. For guides to the original literature on quantum field theory, there are a n-tuber of other books with extensive references that you can consult; these include Peskin Schroeder, Weinberg, and Siegel. (Italicized names refer to works listed in the Bibliography.) Unless otherwise noted, experimental numbers are taken from the Review of Particle Properties, available online at http://pdg.lbl.gov. Experimental numbers quoted in this book have an uncertainty of roughly :t:1 in the last significant digit. The Review should be consulted for the most recent experimental results, and for more precise statements of their uncertainty.
　　To conclude, let me say that you are about to embark on a tour of one of humanity's greatest intellectual endeavors, and certainly the one that has produced the most precise and accurate description of the natural world as we find it. I hope you enjoy the ride.