A First Course in String Theory [ハードカバー]

This book indeed does the impossible, for it introduces, at a level accessible to undergraduate physics and mathematics students, a subject that ranks as the most formidable construction ever attempted in mathematical physics. Using highly esoteric mathematical concepts, string theory, and its modern metamorphosis, M-theory, requires a high concentration of mental effort and long periods of time to assimilate. It has been difficult for students and those who are curious about string theory to find books or papers that are effective in explaining it from a perspective that gives insight into its many intricacies. This book is one of the few that does that, and it deserves the highest ranking of any of the books in mathematical physics that are currently in print. The author, a noted contributor to the field, has produced a book that will certainly motivate many to take up the subject of string theory, and these individuals can be introduced to it early in their education, instead of having to wait for the second or third year of graduate school. In addition, professional mathematicians can gain the needed physical insight from the perusal of the book, and then apply their unique talents and perspectives to extending the frontiers of string theory, which, to emphasize again, is a subject that requires a tremendous amount of mathematical knowledge and skill. Hopefully this book will be used in the university so as to give students an appreciation of the most complex and fascinating theories ever constructed in the history of physics.

The author's strategy is to introduce the reader to string theory by studying physics in high dimensions. This is done early on, by studying Lorentz invariance in more than three spatial dimensions, and by discussing the notion of `compact' dimensions. In addition, the author studies the quantum-mechanical square well problem with an extra (compact) dimension. This example gives the reader some insight into what can happen to the quantum-mechanical spectrum when a compact dimension is present. Throughout the book, the author makes use of light-cone coordinates, which masks to a large extent the relativistic covariance of the theory, but does have the advantage of making the quantization of the string straightforward. The peculiarities of light-cone coordinates are discussed in some detail, but the author explains them in a way that alleviates any doubt as to their use and physical meaning. The author does devote an entire chapter to the treatment of covariant quantization however. In this discussion the reader will get a first look on how difficult it is to quantize a system with constraints, this giving rise to the famous Virasoro operators. The covariant quantization of strings treats of course all coordinates the same, and this introduces the reader to another surprise from the standpoint of the traditional formalism of quantum mechanics, namely that the usual Hilbert space constructions are not valid, since the states that are constructed can have negative norm. In addition, the author is not able to derive the critical dimension in his treatment of covariant quantization since he wants the book to be accessible to undergraduates.

Another virtue of this book is that the author does not expect the reader to remain passive when reading the book. Short exercises and "quick calculations" are dispersed throughout the chapters so as to reinforce the reader's understanding of the topics. In addition, there are good problem sets at the end of each chapter. The "quick calculations" are fun to work out and also serve to slow the overly eager reader from rushing ahead before some of the more fundamental concepts are mastered.

The discussion on D-branes makes the reading of the book especially worthwhile, due to its clarity and the insights it grants on the physics. The role of Neumann and Dirichlet boundary conditions is readily apparent throughout. Due to the use of light-cone coordinates, the author is not able to treat the quantization of strings attached to D0-branes. The appearance of gauge fields (in this case Maxwell fields) when quantizing open strings on Dp-branes is brought out in detail. In his treatment of the quantization of open stretched strings between parallel Dp-branes, the author points out the need for using noncommutative geometry. Noncommutative geometry has received a lot of attention in recent years due to this connection with string theory. The author of course cannot bring in this kind of mathematics without departing from the level of the book. The origin of the Chan-Paton factors as being labels of D-branes, and not merely a computational strategy for obtaining Yang-Mills theories from open strings, is discussed briefly.

The author is quite aware of the skepticism expressed by newcomers to string theory on its physical relevance and experimental realization, for he makes a concerted effort to deal with the extent to which string theories can at least give the results of the Standard Model. He discusses the various approaches to string phenomenology, such as compactification via Calabi-Yau spaces and models based on M-theory. The author recognizes that there is much to be done in string phenomenology, but that significant progress has been made. His remarks should motivate many to enter the field with the goal of showing the derivation of the Standard model from string theory.

T-duality, certainly one of the most fascinating subjects in string theory, is given ample treatment in this book, and its physical interpretation made crystal clear. The presence of T-duality has been of great interest to mathematicians, because it is an example of what has been called `mirror symmetry', a topic that readers will encounter later on if they decide to pursue more advanced treatments of string theory.

Those readers who have encountered Born-Infeld electrodynamics in their travels through physics might be surprised to learn of its applicability in string theory. Being a nonlinear theory of electrodynamics, the Born-Infeld theory is usually thought of as being an historical curiosity. The author shows in detail, using T-duality, how Born-Infeld electrodynamics governs the electromagnetic fields on the world-volumes of D-branes.

Highly recommended!
Dr. Zwiebach's book is an excellent resource for individuals with at least an undergraduate education in physics who are interested in pursuing string theory and related topics. Advanced students in other disciplines can also benefit with some hard work. It is very well organized, starting with the necessary mathematics and relativistic formalism/notation later used in calculations. The book is very rewarding, leading the student with great detail through derivations and avoiding the common "it can easily be shown that..." statements found in other books. The most enjoyable thing is that you really can begin grasping the basics of string theory and branes. After going through this book (maybe in a one year course) the reader should be prepared enough to start looking at other books such as Hatfield, Polchinski, and Green et. al.

Zwiebach has written a book on string theory specifically for advanced undergraduates, and on this merit alone, there is a temptation to give many stars to this text, and this I believe is reflected in the existing reviews. Well deserved praise to Zwiebach for performing this valuable service for the physics community. It will be especially useful to serious undergraduates on helping them decide on whether or not to embark on string theory as a field of research. It provides a faster than normal overview into the subject. Instead of having to invest years in learning the subject, and then (maybe) decide if you do or don't believe this is the correct approach to unification of the fundamental laws, you can decide (maybe) sooner than later if your research efforts could have been directed to greener pastures, or if you are indeed safely on the path to the `holy grail' of physics.

Traditionally, advanced topics in theoretical physics require an undergraduate to first prepare himself with a firm grounding in classical physics (mechanics, EM, thermal, relativity) and quantum mechanics, and a solid grounding in mathematics. Then, after a certain maturity is achieved, the student can study Quantum Field Theory and general relativity and then, finally, string theory.

Zwiebach is attempting to shorten and the even circumvent the traditional learning curve. One might ask, is this possible and if so how? The method Zwiebach uses is to start with introducing 4-vector notation, and explain how to calculate in local coordinates. This is similar to the approach in many field or gauge theory texts, which is not a surprise since they also rely on 4-vector notation. No tensor analysis or differential geometry is provided, but this is fine for this level of a text. After the 4-vectors are introduced, the standard advanced topics are developed as needed. (Lagrangians, Hamiltonians, Maxwell, etc) Finally, the advanced concept is generalized to higher dimensions and the string theory analog is studied.

This approach works to explain the theory on a very elementary level, which was the intent, and the student is able to naively calculate in local coordinates.

I found it slightly annoying that Zwiebach seems to constantly overstate the case for string theory, or else he gives that impression because does not bother to address concerns sufficiently that any bright undergraduate would naturally have, and it is a tone that is present throughout the text. For example (there are more than a few, but for brevity, I list only one example): He says "Are we sure that string theory is a good quantum theory of gravity? There is no complete certainty yet, but the evidence is very good". (pg. 7) A scientist must be objective and explain the good and bad aspects of the theory with a dispassionate objectivity, and doubly so when there are no experiments to moderate one's theoretical speculations. The experimental fact is we don't observe 10 dimensions in the lab (i.e., we only still see 3 space and one time coordinate). The experimental fact is we don't observe compactification of dimensions as physical phenomena. There is zero evidence for this compactification, and this compactification explanation is almost epicycle in nature, as a way to explain why we don't observe those 10 dimensions to begin with. By contrast, Polchinski in his "String Theory", vol. 1, explains how the curling up, or compactification, is consistent (i.e., it is not forbidden) with the geometry of general relativity, since in GR, space-time is dynamic. Also by comparison, Kaku in his "Introduction to Superstrings and M-Theory" seems to take the objections to string theory more seriously, and presents a nice list of the more important objections to the theory. Kaku's book, incidentally, would be a rival text for Zwiebach at the advanced undergraduate level, except it does not have exercises at the end of the chapters, and so is more useful as a reference.

At times, it seems Zwiebach demonstrates occasional lapses in physics erudition...We are informed on page 32 that Planck's constant first appeared in the famous E= (h-bar) w equation, where w is the angular frequency of the photon. Even Freshman physics courses teach Planck was quantizing oscillators in 1900, and Einstein's theory of the photoelectric effect in 1905 (for which he later received the Nobel Prize) where the photon was introduced, was more than a few years away. We are told that the Born-Infeld and related nonlinear theories are as fundamental as the Maxwell equations, if not more so. This is a more advanced error, but amazing nonetheless. Maxwell is a classical, non-quantum theory only. The Born-Infeld equation attempts to explain nonlinearities that are quantum mechanical in nature, where Maxwell does not apply. This is explained even in the introduction to Jackson. Born-Infeld and the related non-linear theories also have an upper bound on the field strength, which Maxwell does not. Coincidentally, the electric fields on D-branes also have an upper bound, so now you can guess as to why Born-Infeld has been elevated to the same status as Maxwell -- because Born-Infeld agrees with string theory, of course. I expect gaps in the rather varied and advanced mathematics one must know, but not in such basic physics --how does this happen at MIT, and in a Cambridge University text? My guess is that string theory is a very demanding mistress, to the point that only strings and mathematics can be concentrated upon, sometimes unfortunately, to the detriment of equally important areas of physics. Perhaps this should be a consideration at least, for the budding undergraduate string theorist.

Despite the bias and the occasional lapses, a good text. Recommended.