Customer Reviews

A First Course in String Theory

5 star:		(17)
4 star:		(3)
3 star:		(2)
2 star:		(0)
1 star:		(0)

 

 

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.

This book provides a clear and up-to-date introduction to string theory. Although the book is suitable for undergraduates, there is a fair amount of background knowledge required, including: electromagnetism, special relativity, and quantum mechanics. I also think exposure to general relativity would be useful since some of the material relates to linearized gravity and some to black holes. Lagrangian and Hamiltonian methods are also used frequently, without a background in these readers might be confused when seeing things like the canonical momentum. All-in-all undergraduates studying this book should probably be fairly advanced, third or fourth year students. Also, this book is not just a simplified version of Polchinski or Green/Schwartz/Witten, the approach is different and I believe valuable even to someone that has already studied these.

The first three chapters give a quick overview of the motivation for string theory and reviews of electromagnetism, special relativity, and quantum mechanics. Readers should probably already be familiar with most of this material, the presentation here is along the lines of a review. Also, some of the material here isn't covered in a typical course on electromagnetism, such as light-cone coordinates (the light-cone gauge is used extensively in the book) and the effects of higher dimensions on the coupling constant. These chapters are followed by a chapter covering an even more basic topic, a classical vibrating string.

After showing relativistic particle action is the length of the particle worldline, the author develops the relativistic string action as the area of the worldsheet, i.e. the Nambu-Goto action. At this point most presentations introduce the Polyakov action. Interestingly, in this book the Nambu-Goto action isn't rewritten as the Polyakov action until close to the end of the book. Another interesting thing is that Zwiebach introduces D-branes here! Following this more results motivated by analogies with classical strings are derived.

An extensive discussion light-cone gauge for relativistic particles, electromagnetic fields and linearized gravity paves the way for quantizing open strings, which is done in light-cone gauge. These results are also leveraged for quantizing closed strings. The usual things like Virasoro operators, critical dimension and tachyons are covered. There is also more discussion of D-branes, D- branes are covered very thoroughly in this book. This concludes the first part of the book, the remainder of the book is devoted to developing more advanced applications of this material.

The first chapter of part two develops D-branes in more detail. The next chapter considers electric charge, antisymmetric field (Kalb-Ramond) charge, D-branes and how they are all interconnected. The analogy between electric charge and the Kalb-Ramond charge of string theory was very illuminating and it's not something one typically sees. Here and in other places in the book the interplay between D-branes and electric fields is described in great detail. This chapter also considers the possible connection between D-branes and the standard model, both the gauge fields and the fermion content. The possibility of the internal dimensions forming a Calabi-Yau space is only briefly mentioned without any details. In fact, Calabi-Yau spaces aren't even defined, this is something that is usually included in most discussions of connections between the string theory and the standard model. On the whole, the discussion of phenomenology is fairly extensive.

The next chapter covers string thermodynamics and black holes. Before turning to black holes there is some general discussion of string theory thermodynamics, among the results is that the Hagedorn temperature is derived. First Zwiebach gives a qualitative argument that string theory gets the Schwarzschild black hole entropy correct to within a multiplicative factor. Then a more precise calculation is done for an extremal five-dimensional black hole, the string theory counting of states is found to agree with the black hole entropy (as the area of the horizon). This is another part of the book where a background in general relativity would be useful.

The next two chapters develop with one of the interesting symmetries of string theory, T-duality, for both open and closed strings. Other duality symmetries of string theory are not considered, not surprising since supersymmetry is hardly mentioned. The following two chapters deal with electromagnetism, more details of D-branes and non-linear (Born-Infeld) electrodynamics.

The final two chapter cover topics that are usually covered much nearer the beginning, covariant quantization and scattering amplitudes. I was fairly surprised to see the Polyakov action covered so late in the book. The material presented is fairly typical, for example: the Virasoro algebra, physical states and moduli.

Overall I think this is a very good book. It's not just a simplified version of Green/Schwartz/Witten or Polchinski, the approach is different and illuminating. Two of the things that stand out are that there is a lot of material on D-branes (especially the connection to electromagnetism) and the approach to phenomenology is interesting. Some important topics are hardly mentioned, supersymmetry and Calabi-Yau manifolds come to mind. However, this isn't a criticism, it would be impractical to try and cover everything of interest.

My interest in String theory arose 3 years ago reading Smolin's book "Three Roads to Quantum Gravity". I knew I couldn't understand the math of String Theory so instead I spent two years preparing by learning Quantum Field Theory and Differential Geometry - then Zwiebach's book came out. There were three issues that I wanted to understand 1) How did string theory actual produce a framework for the standard model, 2) What was the connection between string theory and black holes and 3) How was it that small distances could be indistinquishable from large distances.
First Course delivered nicely. Part 1 - Basics took some effort not only because the material was new but also because it was not motivated, ie. I did not understand why I was studying the material, I did not understand where it was leading. A little trust and faith went a long way though because then I got to Part 2 - Developments where chapters 15, 16 and 17 addressed the topics I was interested in beautifully. In addition my interest in string theory now extends into other areas for example Maxwell fields on D-branes. I'll be going back over Part 1 - Basics soon since I feel I will get a lot more out those chapters having digested Part 2 - Developments. A great book and one I'm grateful for as how many readable introductions are there? - not many!

I used a draft version of this book in the undergraduate string theory class the author teaches at MIT. Prof. Zwiebach wrote this book with a very good pedagogical style, explaning everything step by step, making sure you develop the mathematical tools you need along the way, and, most important of all, MOTIVATING every step leading to the theory.
Reading the book is very rewarding, specially as one is led towards astonishing results that one would think are too hard to understand for an undergraduate student with little experience on advanced theory (for example, how a string theory requires 26 dimensions in order to be consistent).
As an added bonus, this book provided me with an excellent introduction to topics I later found essential when taking graduate courses in Quantum Field Theory, General Relativity, etc. This book should be on the bookshelf of every theoretical physics enthusiast.

This is a wonderful book for someone just learning string theory. I'm trying to do all the problems and many of them are quite tough (I have a PhD in physics.) The thought
that these problems are assigned to undergraduates at MIT is somewhat depressing - either I'm getting senile or they are awesomely talented. Maybe a little of both.
I wish I could get a hold of the solutions (which are available to instructors). Many of the problems teach things about theoretical physics IN GENERAL which I wish I had learned
as an undergraduate (or even as a grad student.)
One of the negatives in struggling with this material is the thought that string theory is really just a step toward M-theory, which is the best candidate for a "theory of everything."
One has to master four or five different string theories and then be told that strings are really not relevant to the currently accepted theory. Since I am retired and have plenty of time, I will continue to struggle with it, but it takes plenty of patience.
In the hands of an instructor who can review (or present solutions) to the problems, this is a wonderful book.
Congratulations to Professor Zwiebach for producing a great text.

Until chapter 10, the book is a pleasure to read. It is very systematic, everything is explained in great detail, and the different concepts are very clear and well exposed. The author succeeds in turning a rather obscure scientific topic into an exciting adventure. If I should judge the book only for this first part, I would give it 5 stars. In fact the book is misleading since when you start reading, you get the illusion string theory can be made accessible even for beginners with an average background.

However, this illusion is in vain since the panorama changes dramatically in chapter 10, where the author enters directly into quantum field theory, without any further preparation. An this is the real problem, because the author who developed from the ground up the classical approach to strings mechanics, takes for granted the reader is highly knowledged in quantum mechanics. In spite of his efforts to introduce the subject in successive approximations, all is in vain because the subject is too intricate. The book is not any more systematic for readers lacking adequate quantum theory background.

Certainly this is not a book for beginners. The book requires previous deep understanding of quantum mechanics. Beginners can still learn some interesting concepts from the first part of the book, but a complete reading would require deep study of less advanced quantum mechanics bibliography. That said, I must also point out if the level of the book is maintained in its second part, it may become a top ten for more advanced readers.

I really cannot recommend this book more highly. The way it approaches a subject that is considered so formidable, the attention to detail, the painstakingly explicit calculations... And the fact that it doesn't just try to sell you a bunch of difficult math as a physical theory, but it actually explains the motivation of every abstract construction it introduces... Perfection! This is the way every physics book should be written. I don't know if there is a chance of this happening, but if Zwiebach ever attempts to write something similar for Field Theory, it will be a blessing.

The first half of the book is also a must read for every physicist, even if you don't know (or wish to know) about string theory. It includes among other things, a truly incredible way to explain the number of degrees of freedom of quantum fields depending on their spin, using light-cone coordinates to write the equations of motion. I haven't seen this anywhere else. This is the way this topic should be taught in field theory courses and I wonder why it isn't more widely used. The book is generally full of such "this really makes sense" kind of epiphanies that will help you understand more fully other things that you used to find confusing or poorly explained elsewhere.

One of the best physics books ever. Really makes one wonder what is wrong with most of the other physics authors.

This book is exactly what it claims to be - a first course in string theory. If you have expectations much beyond a basic introduction to this topic you will be disappointed.

You will need a good understanding of general relativity (space-time metrics, light-cone past/present/future, gaussian coordinates, etc.) this will be a good introduction as to how string theory incorporates both the fundimental classical (relativistic) and quantum-mechanical concepts.

If you have no familiarity with relativity you will struggle with this book because the understanding of reference frames (and the transformations from one to another) is crutial.

As a result, an upper division physics major should be able to follow the math and related concepts while an upper division chemistry or math major would probably struggle with the material .

The problems presented throughout the chapters are clearly the result of this course having been used in the field and a graduate/post graduate physics student may find them coorespondingly simple or naive.

Again, this book is written with the upper-division physics student in mind.