String Theory, Vol. 1 (Cambridge Monographs on Mathematical Physics): Volume 1 Paperback – 20 Jun 2005
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'… this is an impressive book. It is notable for its consistent line of development and the clarity and insight with which topics are treated … It is hard to think of a better text in an advanced graduate area, and it is rare to have one written by a master of the subject. It is worth pointing out that the book also contains a collection of useful problems, a glossary, and an unusually complete index.' Physics Today
'… the most comprehensive text addressing the discoveries of the superstring revolutions of the early to mid 1990s, which mark the beginnings of 'modern' string theory.' Donald Marolf, American Journal of Physics
'Physicists believe that the best hope for a fundamental theory of nature - including unification of quantum mechanics with general relativity and elementary particle theory - lies in string theory. This elegant mathematical physics subject is expounded by Joseph Polchinski in two volumes from Cambridge University Press … Written for advanced students and researchers, this set provides thorough and up-to-date knowledge.' American Scientist
'We would like to stress the pedagogical value of the present book. The approach taken is modern and pleasantly systematic, and it covers a broad class of results in a unified language. A set of exercises at the end of each chapter complements the discussions in the main text. On the other hand, the introduction of techniques and concepts essential in the context of superstrings makes it a useful reference for researchers in the field.' Mathematical Reviews
'It amply fulfils the need to inspire future string theorists on their long slog and is destined to become a classic. It is a truly exciting enterprise and one hugely served by this magnificent book.' David Bailin, The Times Higher Education Supplement
This 1998 volume provides a comprehensive account of the bosonic string, introducing the central ideas of string theory, based on the Polyakov path integral and conformal field theory. This is an essential text and reference for graduate students and researchers interested in modern superstring theory.See all Product Description
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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.
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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