A First Course in String Theory

Rating:
Summary: Didactic perfection
Review: 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.



Rating:
Summary: Strings Everywhere
Review: 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.

Rating:
Summary: excellent
Review: This is one of those books where it isnt expected that the reader already knows the stuff inside out. Instead the book slowly builds intuition and knowledge and is extremely clear. I dont think i have seen clearer explanations anywhere, not even in popular books. For example the way it shows how extra dimensions are compactified is very clear etc. In several places
it shows full calculations (though there are exercises of course). To be honest i am not so interested in string theory, and i have only read the first 170 pages but i can tell its good even if you arent interested in string theory. One can learn a bit of Lagrangian mechanics and quantum field theory from this book as well.

Prerequisites are at least (a little bit of) Lagrangian mechanics and partial differential equations (for example wave equation which is derived from Lagrangian), a little bit of quantum mechanics and special relativity.


Rating:
Summary: A must read for non-geniuses
Review: Unless you are the next person after Einstein and Witten this book will find use with you. The author shows his brilliance and deep understanding in the way he can teach this stuff without any convolution. Very highly recommended.