Superstring Theory: 25th Anniversary Edition (Cambridge Monographs on Mathematical Physics) (Volume 1) Anniversary Edition

I have just finished reading and studying Volume 1 of Green, Schwarz and Witten, it is extremely well written the first four chapters I understood them straight away, the first one gives you an historical introduction into the subject as how strings were used in the early seventies for modeling the strong nuclear force and the Veneziano Amplitude. Details are give as how the different conformal mappings of the string worldsheet can be mapped to the whole plane or half plane (depending wether you have a closed or open string) and how the different values of the points (0,1,infinity) contribute due to the conformal symmetry that the theory has. It is important at this stage to point out that the book by Kiritsis ("String Theory in a Nutshell") does not give you any hint of why the infinite value of the variable does not contribute. But GSW explains it beautiful. The only problem is when you have a Tachyon in which case you have a divergence in the amplitude of scattering on top of dealing with a particle which is nonsensical since it has imaginary mass. The second chapter introduces the Bosonic String, both the open and closed case and the various conditions for the boundaries and vibrational modes propagating on them. Here it is shown that the Bosonic String has a tachyon and that the theory only makes sense in the critical dimension D=26. Also the light-cone gauge and old covariant methods of quantization are presented. Chapter three gives the more new method of BRST quantization, it explains how you construct the BRST charge and that the physical states are anhilated by it. Here are given the action of the ghosts that are brought with the BRST and how they again imply D=26. Chapter four is about the superstring applying supersymmetry to the world-sheet coordinates, the usual SUSY transformations are given for the bosonic coordinates and for the new fermionic ones who happen to be Spinors in the worldsheet. A word of caution the SUSY transformations only close on-shell but then using the superspace technique an auxiliary field is introduced who fixes everything and has no dynamics. Chapter five is about applying Supersymmetry to the spacetime and the problem here is that the book begins to get more involved in the formalism. For example the Superstring now has equations of motion so complicated they can only be resolved in light-cone gauge again the BRST is applied and now as a result we have more ghosts but this time bosonic associated to the fermionic coordinates. With SUSY the tachyon is shown to disappear and the critical dimension is now D=10 for Lorentz invariance and conformal invariance and susy. Chapter 6 deals with the way to incorporate internal gauge degrees of freedom like giving quantum numbers to the two ends of the open string or separating the Fermionic spinors into one which live in one representation and other group in another thus creating the Heterotic String with SO(32) or E8xE8 gauge symmetry. Finally chapter seven is a lot of crap (excuse me) for how you can build the tree amplitudes of scattering for the different strings. AH! and by the way Type I refers to having Supersymmetry with N=1 and 32 supersymmetric charges and Type II (A and B) for SUSY with N=2 and 64 supercharges. Type II A also has left and right chiral fermions while Type II B has only one type of chirality. The amplitudes are presented first for the bosonic open and closed string and then for the Ramond Neveu Schwarz model of the superstring (the approach of chapter 4) and finally the explicit superstring in the spacetime, both superstrings have critical dimension D=10. Here are constructed the various vertex operators that are needed for inserting legs to the string diagrams, the ones for the Bosonic case are more or less self evident but you need to have more care for the Vertex operators of the Fermionic states in the superstring specially in the last case that refers to the strings of chapter 5, some of the last things I just skipped because it gets really awful for a first reading. I am now prepared to delve into the Second Volume specially because on the mathematical side I am already acquainted with most of the differential geometry and algebraic topology which are reviewed in chapters 12 and 15!! (although no algebraic geometry on my wallet!) All in all a great read and the only book that has permitted me to go through the theory of Superstrings in depth although I had already read the half of the undergraduate introductory text of Zwiebach and another one called "String theory demystified" both of them dealing only with the Bosonic string, so this going of Green Schwarz and Witten has been my first attempt to go through the SUPERSTRINGS, so my recommendation, go first with Zwiebach, then MacMahon (demystified) and then with this volume and it will be I hope as it has been to me SUCH A GREAT ADVENTURE!, can wait to read the second volume, these guys (Green, Schwarz, Witten) really know their subject and they do it well, A MUST for any physicist thinking on going as me to go IN Superstrings Theory which by the way is the only theory that has predicted GRAVITY at the quantum level and in a consistent though surprising way, A MUST!!.............

Very good condition

At one time volumes I and II of "Superstring theory" would have been essential reading for serious students of string theory. However, the way we think of string theory today is very different from the way it was formulated in these classic texts. The core is still the same, but the advent of D-branes, various dualities and M-theory have radically changed the way we see string theory. This is not to mention all the other progress in string theory such as the extensive work on black hole physics. Still this book should not be missed.Volume I stands on its own as an excellent introduction to superstring theory. However, other than showing general relativity appears in the low energy limit of string theory, potential observable consequences are mainly put off until volume II. Most of the arguments for the physical relevance of string theory are based on self-consistency and finiteness.Following a historical tour of the origins of string theory as a dual model, the main topic is introduced, string theory as a candidate for the quantum theory of gravity and providing a grand unified field theory. The obvious question, what makes a theory based on one-dimensional objects is better than one based on zero-dimensional objects, is thoughtfully considered. Several arguments are given. The first chapter closes out with an overview of string interactions.Starting with the simple physical idea that the action of a string is the area of the worldsheet, the authors develop bosonic string theory. Different approaches to quantizing strings in flat spacetime are presented with two of the main results being the calculation of the critical dimension and the central change.The flat spacetime calculations are generalized to a curved spacetime. The low energy effective action is derived, with the amazing result that in this limit string theory reproduces general relativity. Conformal invariance clearly plays an important role throughout this, but general conformal field theory is never explicitly developed. I would have liked to seen is a more explicit treatment of general conformal field theory, but that's a matter of personal taste. All this is done in less than 200 pages!The book then moves on to cover superstring theory. From this point on bosonic and superstrings are considered in parallel where appropriate. It starts off adding fermions onto the worldsheet. This theory is quantized in an approach that parallels that of the bosonic string (operator expansion, light-cone gauge, BRST). It then moves on to show the connection of worldsheet supersymmetry to spacetime supersymmetry.The types of superstrings developed are Type I, Type IIA, Type IIB and heterotic (with various gauge symmetries). As a side note on perspective, these are described as different string theories, but the advent of M-theory they are currently seen as different solutions to one theory.The book wraps up with very through calculations of tree level scattering amplitudes.Undoubtedly this is an excellent book. The only questions are, "How well does it hold up, is it still essential reading"? It definitely holds up very well. I consider it essential reading, however I think the point could be argued. I doubt anybody would argue that people specializing in string theory would profit by reading it.

Classic must-have