Superstring Theory: Volume 1, Introduction (Cambridge Monographs on Mathematical Physics) 1st Edition

by Michael B. Green (Author), John H. Schwarz (Author), Edward Witten (Author)

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ISBN-13: 978-0521323840

ISBN-10: 0521323843

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In recent years, superstring theory has emerged as a promising approach to reconciling general relativity with quantum mechanics and unifying the fundamental interactions. Problems that have seemed insuperable in previous approaches take on a totally new character in the context of superstring theory, and some of them have been overcome. Interest in the subject has greatly increased following a succession of exciting recent developments. This two-volume book attempts to meet the need for a systematic exposition of superstring theory and its applications accessible to as wide an audience as possible.

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Editorial Reviews

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"...extremely useful to the beginning student..." Donald Marolf, University of California Santa Barbara, American Journal of Physics

Book Description

This two-volume book attempts to meet the need for a systematic exposition of superstring theory and its applications accessible to as wide an audience as possible.

Publisher ‏ : ‎ Cambridge University Press; 1st edition (January 30, 1987)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 478 pages
ISBN-10 ‏ : ‎ 0521323843
ISBN-13 ‏ : ‎ 978-0521323840
Item Weight ‏ : ‎ 8.1 ounces
Dimensions ‏ : ‎ 2.03 x 7.34 x 9.5 inches

Best Sellers Rank: #3,568,122 in Books (See Top 100 in Books)
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John H. Schwarz

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Reviewed in the United States on March 15, 2017

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This is a great book, and the costumer service is very good.

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A TEXTBOOK SUMMARIZING “THE PRESENT STATE OF KNOWLEDGE”

Reviewed in the United States on July 22, 2020

The authors wrote in the Preface of this 1987 book, “Recent years have brought a revival of work on string theory, which has been a source of fascination since its origins nearly twenty years ago. There seems to be a widely perceived needed for a systematic, pedagogical exposition of the present state of knowledge about string theory. We hope that this book will help to meet this need… We hope that these two volumes will be useful for a wide range of readers, ranging from those who are motivated mainly by curiosity to those who actually wish to do research on string theory. The first volume… gives a detailed introduction to the basic ideas of string theory. This volume is intended to be self-contained… We feel that the two volumes should be suitable for use as textbooks in an advanced graduate level course.”

They note, “The real hope for testing quantum gravity has always been that in the course of learning how to make a consistent theory of quantum gravity one might learn how gravity must be unified with other forces. A consistent unified theory of gravity and other forces might someday confront experiment through its implications for already measured quantities like the mass of the electron or the Cabibbo angle or by predicting new phenomena at high but accessible energy scales…” (Pg. 14)

They suggest, “Nowadays, we know that electromagnetism and gravity are far from being the whole story. A satisfactory unified theory must accommodate a good deal more. In fact, five dimensions are not enough; with ten we might just manage. If dual theories are viewed as a way of making sense of quantum gravity, then the fact that the dual model of bosons and fermions makes sense only in ten dimensions has the earmarks of a blessing in disguise, a hint that dual models are not just consistent theories of quantum gravity but consistent unified theories of all interactions.” (Pg. 16)

They explain, “Now we are ready to discuss strings. The string is a one-dimensional object, a mathematical curve. We consider both open strings, which have endpoints, and closed strings, which from a topological viewpoint are circles… To describe the motion of a string it is useful to introduce in addition a timelike evolution parameter ‘r,’ which is a sort of time coordinate for an observer sitting at the position ‘o’ along the string. As the string propagates in space-time… it sweeps out a world sheet that is the generalization of the world line of a point particle.” (Pg. 21-22)

They point out, “historically, in the case of general relativity, it was the concepts that came first; Einstein first identified the concepts on which a relativistic theory of gravity should be based, and then found the theory. String theory has been the other way around… string theory was originally invented for other reasons entirely, in an unsuccessful assault on the strong interactions. It eventually became clear that string theory should be used, instead, to give a fundamental generalization of general relativity and Yang-Mills theory. But the concepts behind this generalization remains largely mysterious. At best we have perhaps just begun to scratch the surface of this question. For this reason the stringy generalization of Yang-Mills theory and gravity, though we know much about it, is indicated by a question mark in fig. 1.4. The missing circle of ideas is bound to one day have a far reaching impact on physics, and perhaps on certain branches of mathematics.” (Pg. 26-27)

They observe, “Equation (1.4.4) should seem like a rather startling formula. In (1.4.4), a scattering amplitude in 26-dimensional space-time is expressed in terms of a correlation function in an auxiliary (1+1)-dimensional quantum field theory. According to the standard LSZ formalism of quantum field theory, correlation functions in a (1+1)-dimensional world. That they can be interpreted instead to give scattering amplitudes in 26 dimensions is one of the wonders of string theory. It is one of many surprising and still largely mysterious relations and analogies between phenomena that occur on a string world sheet and phenomena that occur in space-time.” (Pg. 36)

They acknowledge, String theory is certainly an unusual approach to formulating a relativistic quantum theory, and one consequence of this is that, while the rules we have sketched for calculating scattering amplitudes are manifestly Lorentz invariant, it is not too obvious that unitarity will be obeyed. In fact, in studying unitarity one finds a number of surprises. Among them is the restriction to ten or 26 dimensions, of which we will give a proper account in the following chapters.” (Pg. 52)

They state, “Thus, we conclude that physical states in the bosonic theory are BRST cohomology classes of ghost number -1/2. Actually, to complete the proof of this statement we must establish the converse of this statement… Though it is rather clear that this is true, a really complete and economical proof does not seem to have appeared as of this writing, and we will not try to prove it here.” (Pg. 138)

They say, “The condition for vanishing ‘B’ function is certainly needed in string theory… and this condition must coincide with the equations of motion if it is to have any sensible physical interpretation. Therefore, in hindsight, we should breathe a sigh of relief that the condition (3.4.2) for vanishing of the lowest-order ‘B’ function has a sensible interpretation as a long-wavelength approximation to the equation of motion of the gravitational field. Equation (3.4.20) must have such an interpretation is string theory is to make sense.” (Pg. 172)

They note, “We have also discussed the dynamics of a string in the presence of background fields, including a nontrivial space-time geometry. By requiring that the two-dimensional world-sheet theory be conformally invariant, even at the quantum level where anomalies in the trace of the two-dimensional energy-momentum tensor must vanish, we learned the background fields must satisfy the field equations of the string theory itself. This implies a subtle self-consistency between the background fields that determine the dynamics of the string and the dynamics of the string whose solutions determine the possible background fields. The understanding of these connections, which are surely of fundamental importance, is still being developed.” (Pg. 184)

They comment, “the GSO projection … gives a supersymmetric theory (in the ten-dimensional sense, to be contrasted with the two-dimensional supersymmetry that is already present). We shall see evidence for this here, and a complete proof in the next chapter. Space-time supersymmetry is an elegant and attractive thing, and on these grounds alone the GSO projection is attractive.” (Pg. 219)

They state, “The description of superstrings given in chapter 4 suffers from one striking drawback. It is extremely difficult to understand the origins of space-time supersymmetry. Bosonic strings are described by choosing one set of boundary conditions and fermionic ones by choosing another set. Then, lo and behold, there is a symmetry relating to the two sets of states. It is certainly necessary to have this symmetry, as we have already argued, to have consistent interactions of the gravitino field contained in the massless closed-string multiplet.” (Pg. 249)

They suggest, “Pursuing the analysis in this way … does not help to achieve the objective of covariant quantization, however. What should one conclude from all this? There are several different points of view, each of which seems to be preferred by some of the workers in this field… The most ambitious hope would be that there is a clever modification of reinterpretation of the supersymmetric superstring action that allows quantization to be achieved while maintaining the full super-Poincaré group as a manifest symmetry… Such a prospect does not sound unnatural in the string context. Some proposals have been made, but it is still too early to assess how fruitful they are likely to be.” (Pg. 281)

They explain, “If superstrings are to describe nature they must account not only for general coordinate invariance and local supersymmetry, but also for the local gauge symmetries that underlie the other forces. Indeed, nonabelian gauge symmetry is more obviously needed then local supersymmetry. One possibility is that the gauge symmetries are not present at all in the ten-dimensional world, but arise only upon reduction to four dimensions. This idea, which seems to be forced upon us if we try to describe nature with type II superstrings, proves to have enormous difficulties… A more promising possibility is that gauge symmetries are present already in the ten-dimensional world. In this case, compactification from ten to four dimensions may play a role as part of an initial stage of symmetry breaking.” (Pg. 291)

They admit, “The understanding of string theory has not yet been developed to the point where one can write down a Lagrangian and follow a standard prescription to deuce rules for constructing Feynman diagrams that provide the loop expansion of the full quantum theory… There has been recent progress in this direction, but we will not attempt to survey these developments in this book.” (Pg. 354)

They recount, “The proposal to use string theory as a unified theory of fundamental forces including gravitation, rather than as a theory of hadrons, was made by Scherk and Schwarz… They also noted that in this context it was natural to take seriously the extra dimensions of the known string theories… The Kaluza-Klein idea of extra dimensions… has probably been the most imaginative of the early suggestions concerning unification of electromagnetism and gravitation…” (Pg. 436)

This is a fine introductory text, that will be of great interest to those studying superstring theory.

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Should still be required reading

Reviewed in the United States on May 31, 2003

Anyone interested in learning string theory could perhaps start with the current formulation involving D-branes and M theories. This is certainly possible and will lead one to the frontiers of research. However, it would not perhaps give one an appreciation of string theory that would be obtained by persuing a study that explains how it arose in the study of the strong interaction . This book, written by three giants in string theory, will give the reader such a study, and was the first book to appear on the subject. The book is a monograph, and not a textbook, since no exercises appear, but it could still serve as a reference and "required reading" for courses in string theory.
The learning of string theory can be a formidable undertaking for those who lack the mathematical background. Indeed, a proper understanding of string theory, not just a forma one, will require a solid understanding of algebraic and differential geometry, algebraic topology, and complex manifolds. There are many books on these subjects, but I do not know of one what will give the student of string theory an in-depth understanding of the relevant mathematics. These two volumes include two rather lengthy chapters on mathematics, one on differential geometry and the other on algebraic geometry. The mastery of these two chapter will give readers a formal understanding of the mathematics, and will allow them to perform calculations in string theory efficiently, but do not give the insight needed for extending its frontiers. There have been a few books published on string theory since these two volumes appeared, but they too fail in this regard (and some even admit to doing so). To gain the necessary insight into the mathematics will entail a very time-consuming search of the early literature and many face-to-face conversations with mathematicians. The "oral tradition" in mathematics is real and one must embed onself in it if a real, in-depth understanding of mathematics is sought.
The physics of string theory though is brought out with incredible skill by the authors, and the historical motivation given in the introduction is the finest in the literature. Now legendary, the origin of string theories in the dual models of the strong interaction is discussed in detail. The Veneziano model, as discussed in this part, has recently become important in purely mathematical contexts, as has most every other construction in string theory. The mathematical results that have arisen from string theory involves some of the most fascinating constructions in all of mathematics, and mathematicians interested in these will themselves be interested in perusing these volumes, but will of course find the approach mathematically non-rigorous.
Some of the other discussions that stand out in the book include: 1. The global aspects of the string world sheet and the origin of the moduli space, along with its connection to Teichmuller space. 2. The world-sheet supersymmetry and the origin of the integers 10 and 26 as being a critical dimension. In this discussion, the authors give valuable insight on a number of matters, one in particular being why the introduction of an anticommuting field mapping bosons to bosons and fermions to fermions does not violate the spin-statistics theorem. 3. The light-cone gauge quantization for superstrings. The authors show that the manifestly covariant formalism is equivalent to the light-cone formalism and is ghost-free in dimension 10. The light-cone gauge is used to quantize a covariant world-sheet action with space-time supersymmetry, with this being Lorentz invariant in dimension 10. This allows, as the authors explain in lucid detail, the unification of bosonic and fermionic strings in a single Fock space. 4. Current algebra on the string world sheet and its origin in the need for distributing charge throughout the string, rather than just at the ends. The origin of heterotic string theory is explained in this context.

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Classic in every sense

Reviewed in Spain on December 11, 2019

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No brainer. Like MTW or “The Large Scale Structure of Spacetime”, this is another jewel which beauty and value goes beyond the content. You need up to chapter 16 included of Peskin and or alike to be able to even go through the first chapter though.

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Superstring Theory: Volume 1, Introduction (Cambridge Monographs on Mathematical Physics) 1st Edition

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