String Theory, Vol. 1 : An Introduction to the Bosonic String (Cambridge Monographs on...

String Theory, Vol. 1 : An Introduction to the Bosonic String (Cambridge Monographs on Mathematical Physics) | Joseph Polchinski | Very thorough and upto date

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	String Theory, Vol. 1 : An Introduction to the Bosonic String (Cambridge Monographs on Mathematical Physics) Joseph Polchinski Cambridge University Press, 1998 - 422 pages average customer review:based on 9 reviews view larger image
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highly recommended

The two volumes that comprise String Theory provide an up-to-date, comprehensive account of string theory. Volume 1 provides a thorough introduction to the bosonic string, based on the Polyakov path integral and conformal field theory. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory, the Polyakov path integral, and the covariant quantization of the string. The book then treats string interactions: the general formalism, and detailed treatments of the tree level and one loop amplitudes. Toroidal compactification and many important aspects of string physics, such as T-duality and D-branes are also covered, as are higher-order amplitudes, including an analysis of their finiteness and unitarity, and various nonperturbative ideas. The volume closes with an appendix giving a short course on path integral methods, followed by annotated references, and a detailed glossary.

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Enlightening text on a murky topic

This book succeeds in what seems to be the impossible. It actually presents a clear, up to date, and entertaining version of a field that is still very much in a state of active research and is still, after all these years, on quite uncertain ground. By studying this, the reader who thinks intelligently about the material presented will be able to form his/her own opinions on this still somewhat controversial topic and will be able to converse intelligently with others who have opinions on the topic. I know that for me personally, this text opened up beautiful ideas which, to a large extent, are still unexplored. Before I read this book, my gut feelings about the topic were that it was rather dubious at best, but now that I understand (I think) the basic ideas of the field, I feel quite comfortable in it, indeed almost as if it is completely natural. What I think is one of the best things about this book is that it does not assume the pretense that string theory is on firm ground, that everything is quite certain and that string theory HAS to be the final theory of nature in all its glory. I find this attitude EXTREMELY pretensious and annoying. Instead, it simply covers what we know about string theory, and explains in detail just why it is consistent, and why it offers an explanation for what we see in nature. In short, it leaves just enough room for the imagination of an intelligent reader to philosophize as to the meaning of the theory and as to its ultimate place in nature
As for practical details, it seems to me that the reader should at the very least have a firm understanding of Quantum Field Theory (at least at the level of Weinberg's first volume, see my review on that modern masterpiece), and to a lesser extent of General Relativity, before even attempting to tackle this. I know that I myself, despite the fact that I have read several texts on QFT, had to reread several sizeable chunks of the book to fully digest it.

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Very thorough and upto date

The two volumes introduce many important recent developments in string theory not covered in Green, Schwarz & Witten's Superstring text such as D-branes, dualities, etc. However, I found GSW's treatment of basic materials easier to follow because the authors try to explain things intuitively. Although many physical insight in Polchinski's book is sacrificed, it makes up for them through completeness and mathematical rigor. However, I highly recommend that you read Di Francesco et al's conformal field theory book (read chapters 3-7, 10 and 12-13) to get a better feel for stuff like operator state mapping, OPE's, Virasoro algebra, vertex operators, etc. Of course a good course in QFT, GR and some basic familiarity with SUSY, Rep. theory, & some algebraic topology are probably a prereq although Polchinski claims the book is pretty much self-contained. Lastly, the book suffers a little from numerous typos (atleast the 1st edition) but corrections are updated frequently on a ucsb website address.

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The string theory book

In short, I think volumes I and II of "String Theory" are the best books on string theory available. Presumably any serious student of string theory will study them both. The writing style is clear, physical considerations are at the forefront, the selection of topics is excellent and the treatment is as up-to-date as any I'm aware of.

Volume I covers the bosonic string. Of course this doesn't provide a realistic model for our universe, but understanding it forms the foundation of the study of more realistic string theories.

The first chapter provides the physical motivation for string theory. A brief description of some current unsolved problems in physics, and how string theory may resolve them, is given. Most notably this includes not only providing a quantum theory of gravity, but also providing a grand unified theory. A brief outline of techniques used throughout the book is given. These are covered in more detail as the book develops and include: the Polyakov action (how to get it from the Nambu-Goto form and why it's more useful), the Polyakov action symmetries, string theory as a two-dimensional quantum field theory, string boundary conditions, the string spectra, supersymmetry (worldsheet and spacetime) and the critical dimension. This is an excellent introduction and nicely sets the stage for the rest of the book.

The next chapter presents conformal field theory. It's also an excellent introduction. In particular covering conformal field theory with anticommuting fields. The Virasoro algebra is also derived. He could have covered these conformal field theory concepts as they came up, but I liked having them in one central location early in the book.

Strings take center stage again in the following chapter as the Polyakov path integral is examined in great detail. Among the results are a calculation of the critical dimension and the recovery of general relativity in the low energy limit of string theory. These are just a couple of the interesting results, there is much more in this chapter.

The following chapters quantize the string, calculate the string spectrum, derive the S-matrix, calculate tree level scattering amplitudes and calculate one-loop amplitudes (higher order amplitudes are covered in the final chapter). One of many things that stand out is his discussion of divergences. He describes the difference between infrared and ultraviolet divergences. After showing ultraviolet divergences are absent in string theory he comments on how the mechanisms that remove them is different for open and closed strings. This is just one example of how physical concepts are kept at the forefront.

The chapter on compactification covers more than just the basics such as (D - 4) dimensions must be compactified and this gives rise to some extra gauge fields. Orbifolds are introduced in this chapter. It also covers T-duality, one of the important (and unexpected) symmetries of string theories. D-branes are also introduced (D-branes are covered in more detail in volume II), obviously this is an important concept in string theory. I was happy to see such important concepts introduced so quickly.

In short, this is a great book. Even with only light coverage of supersymmetry (this is covered in detail in volume II) many interesting and up-to-date topics are presented. Clearly the author put a lot of time into thinking about how to make a difficult subject as approachable as possible. Throughout the book he anticipates questions the reader may have, or maybe should have, and addresses them.

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Good book, but....

This is an exceptionally well written book of the highest quality. In many ways, it definitely accomplishes what it sets out to do-give graduate level students and professional physicists an advanced string theory book that can prepare them for research. This book is not one that is going to hold your hand. Nonetheless, it is very well written and has a clear and well organized exposition.

Right now, I am writing a string theory book of my own so have been reading and reviewing a lot of books. You will see that most of my reviews are positive. The reason I mention this is that maybe you can take my reviews a little more seriously since I am simultaneously trying to wade through a number of these books.

The notorious "path integral" is of course, a vital component when learning string theory at this level. What I find basically annoying is that nobody, even Polchinski, seems to have found a CLEAR and SIMPLE way to teach people what a path integral is and how to calculate them. I give Polchinski a B+ for his effort in the appendix, but come on people-can't we do better? I have yet to read a description of what a path integral is without 1) Getting a major headache and 2) being able to sit down and calculate them. I think Polchinski or someone else with an inclination to writing textbooks ought to just focus on that-write a small book on path integrals that finally makes this technique accessible to the majority of the human race.

OK so where are you in your string theory program. Just staring out? This is not the book for you. I like Becker, Becker & Schwarz for "beginnners" (I am assuming you have a significant background in math & physics, but maybe you're not a star grad student at Princeton). I also liked the books by Kaku. Once you've gone through Becker et. al. you can tackle this one.

I think just a basic understanding of quantum field theory is all you need, but the stumbling block is going to be the path integral. If you get path integrals, then this book will be a breeze. If you don't, then you're not going to know what the hell he is talking about.

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reviews: page 1, 2

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