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Problem Book in Quantum Field Theory
The Problem Book in Quantum Field Theory contains about 200 problems with solutions or hints that help students to improve their understanding and develop skills necessary for pursuing the subject. It deals with the Klein-Gordon and Dirac equations, classical field theory, canonical quantization of scalar, Dirac and electromagnetic fields, the processes in the lowest order of perturbation theory, renormalization and regularization. The solutions are presented in a systematic and complete manner. The material covered and the level of exposition make the book appropriate for graduate and undergraduate students in physics, as well as for teachers and researchers.
253 pages, Paperback
First published January 1, 2006
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Displaying 1 - 2 of 2 reviews
April 18, 2021
There is, as the author of this book points out, a shortage of books of problems on quantum field theory. This one is based on exercises set to undergraduate and graduate students of the University of Belgrade. There are 64 pages of problems and the solutions occupy a further 171 pages. There is a bibliography and an index. The book would serve well to accompany an introductory course on QFT.
Lewis H. Ryder
Lewis H. Ryder
July 27, 2018
Many great textbooks have been written on Quantum field theory; however, there was a gap in the market which had to do with a problems book. This book fills this gap in a very successful manner.
Each chapter starts off with a very brief overview/review of the knowledge one needs to start doing the problems. Do not expect this to help you learn the material presented there; this is definitely not the job for this section. It serves to remind you of the material you have already studied and also to have it as reference while you are going through the exercises. This is very convenient.
As for the problems, they start off easy and gradually build up to some tough and/or more creative problems. This way of gradually increasing the difficulty is what every problems sections in every textbook should follow: it eases the reader into the more difficult exercises and guarantees that any failure of the reader/solver to solve a difficult exercise originates purely from his/her own possible lack of ability to do so and not from just being thrown into deep waters very early on.
The nature of the problems varies from problem to problem. There are problems whose goal is to just familiarize the reader with some standard calculations that are often found in field theories. Some of these, for example, might have to do with boringly -but necessarily- using commutation (or anti-commutation) relations to play with the creation and annihilation operators to compute something relatively trivial and/or standard. Some of these problems include long (and, often, tedious) calculations that are nonetheless very much needed; otherwise, one cannot be or feel confident enough tackling difficult and long calculations on, say, scattering amplitudes.
Other problems are much more interesting and possibly non-trivial. For example, the last problem of chapter 3(which is on the Dirac γ-matrices) has to do with finding the Dirac matrices in 2 spacetime dimensions. [SPOILER ALERT!] It all comes down to the Pauli matrices, of course, but the problem actually shows you that γ^(5) is in this case only the third Pauli matrix rather than something fancier. It was a nice surprise for me to see such a problem here since I have an extensive condensed matter physics background and I have thus studied the properties of 2D spaces and spacetimes and I have (sadly, but unsurprisingly) found that nearly nobody mentions anything about the chiral representation for less than four spacetime dimensions.
The solutions are very detailed and thorough. Although there are examples of a problem skipping some very small steps, at the end, this is for the better as it never skips hard steps but never gives the full details, something which poses the risk of "inviting" the reader to just check the solutions out when he/she is stuck. All in all, I am very satisfied with the solutions.
One criticism that I have is that the solutions might use some more commenting; not because they need it but because it makes the whole thing more "colorful". For example, the solution to the problem on the Gordon decomposition of the Dirac current (4.21) could use some commenting on how one part of the decomposition has to do with the movement of the center of mass while the other has to do with the spin of the electrons. Saying just that could have made the whole thing much more than an exercise in mathematical manipulations. Had the author also added that the decomposition shows that the interactions involving electrons take place due to the electron's charge but also its spin, would have turned the exercise into something special due to the added insight that the author provides. It would also motivate the students to thoroughly check out the author's solution to an exercise once the reader is done with it.
But, this is all nitpicking. As I said, this book fills in a very important gap and it does not very successfully. My small criticism above has to do with giving the book something extra, besides the main thing that it does so efficiently: to prepare the reader for exams and research and to make him/her feel truly confident about his/her knowledge of Quantum Field theory. Closing, I will say that at the time of completing this review, I found the pricing to be a bit steep. But, if one also accounts for it being the only book on problems and solutions in QFT, then it is not too much. I urge everybody who wants to master QFT to give this a try as I believe that it will serve them well.
Each chapter starts off with a very brief overview/review of the knowledge one needs to start doing the problems. Do not expect this to help you learn the material presented there; this is definitely not the job for this section. It serves to remind you of the material you have already studied and also to have it as reference while you are going through the exercises. This is very convenient.
As for the problems, they start off easy and gradually build up to some tough and/or more creative problems. This way of gradually increasing the difficulty is what every problems sections in every textbook should follow: it eases the reader into the more difficult exercises and guarantees that any failure of the reader/solver to solve a difficult exercise originates purely from his/her own possible lack of ability to do so and not from just being thrown into deep waters very early on.
The nature of the problems varies from problem to problem. There are problems whose goal is to just familiarize the reader with some standard calculations that are often found in field theories. Some of these, for example, might have to do with boringly -but necessarily- using commutation (or anti-commutation) relations to play with the creation and annihilation operators to compute something relatively trivial and/or standard. Some of these problems include long (and, often, tedious) calculations that are nonetheless very much needed; otherwise, one cannot be or feel confident enough tackling difficult and long calculations on, say, scattering amplitudes.
Other problems are much more interesting and possibly non-trivial. For example, the last problem of chapter 3(which is on the Dirac γ-matrices) has to do with finding the Dirac matrices in 2 spacetime dimensions. [SPOILER ALERT!] It all comes down to the Pauli matrices, of course, but the problem actually shows you that γ^(5) is in this case only the third Pauli matrix rather than something fancier. It was a nice surprise for me to see such a problem here since I have an extensive condensed matter physics background and I have thus studied the properties of 2D spaces and spacetimes and I have (sadly, but unsurprisingly) found that nearly nobody mentions anything about the chiral representation for less than four spacetime dimensions.
The solutions are very detailed and thorough. Although there are examples of a problem skipping some very small steps, at the end, this is for the better as it never skips hard steps but never gives the full details, something which poses the risk of "inviting" the reader to just check the solutions out when he/she is stuck. All in all, I am very satisfied with the solutions.
One criticism that I have is that the solutions might use some more commenting; not because they need it but because it makes the whole thing more "colorful". For example, the solution to the problem on the Gordon decomposition of the Dirac current (4.21) could use some commenting on how one part of the decomposition has to do with the movement of the center of mass while the other has to do with the spin of the electrons. Saying just that could have made the whole thing much more than an exercise in mathematical manipulations. Had the author also added that the decomposition shows that the interactions involving electrons take place due to the electron's charge but also its spin, would have turned the exercise into something special due to the added insight that the author provides. It would also motivate the students to thoroughly check out the author's solution to an exercise once the reader is done with it.
But, this is all nitpicking. As I said, this book fills in a very important gap and it does not very successfully. My small criticism above has to do with giving the book something extra, besides the main thing that it does so efficiently: to prepare the reader for exams and research and to make him/her feel truly confident about his/her knowledge of Quantum Field theory. Closing, I will say that at the time of completing this review, I found the pricing to be a bit steep. But, if one also accounts for it being the only book on problems and solutions in QFT, then it is not too much. I urge everybody who wants to master QFT to give this a try as I believe that it will serve them well.
Displaying 1 - 2 of 2 reviews