Book Description
In The Quantum Theory of Fields, Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory emerges from this as a natural consequence. The author presents the classic calculations of quantum electrodynamics in a thoroughly modern way, showing the use of path integrals and dimensional regularization. His account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to elementary particle physics, and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. This work will be an invaluable reference for all physicists and mathematicians who use quantum field theory, and it is also appropriate as a textbook for graduate students in this area.
Customer Reviews:
Very thorough and logical, but somewhat difficult and painful to get through.......2007-07-23
To put the review in perspective, My Background: I am a senior undergraduate engineering/physics student with an interest in mathematics and theoretical physics. This is my third QFT book.
Things I liked about the book:
- The book follows a very logical progression. I love how Weinberg presents a coherent argument based on simple physical principles (specifically Lorentz invariance and the cluster decomposition principle).
- Weinberg takes painstaking effort to avoid hand-waving, and is very careful to enumerate (and make plausible) his assumptions. In so doing, he avoids the sort of black-magic feeling I got when reading some less well written QFT books (see for example: Peskin and Schroeder, which makes a mockery of logical progression in an effort to teach you how to calculate as soon as possible).
- The book was very thorough, and often provided an original approach to the material. The coverage of renormalization seemed natural and coherent, and since the book is presented in a logical order (rather than a historical one) Weinberg avoids justifying renormalization as some mysterious subtraction of infinities, basing it instead on general non-perterbative methods (e.g. poles of the S-matrix, etc...)
What I didn't like about the book:
- As a result of his unwavering emphasis on logical progression, and his inclusion of a vast amount of material (almost all of which is necessary to understand in order to progress through the book), the book is somewhat painful to get through. Be prepared to re-read many of the sections a couple of times, and to make very slow progress.
- Weinberg chooses to present QFT in a very general form (i.e. abstracting it from a particular field such as particle physics or condensed matter physics). This is not necessarily a disadvantage, but I often found my interest waning after reading a few hundred pages without making any contact with phenomenology. Additionally, the excercises were similarly abstract, which makes it difficult (at least for me) to particularly care about their results. (More of a problem for self-study)
- The notation is very complete, which isn't normally a bad thing. However, the equations sometimes become very cumbersome when he includes every index, and every functional dependence regardless of how redundant they may be.
- In his coverage of path integrals, he derives things using functional determinants rather than through the more common generating functional methods. I think this hides a lot of the physical insight of the path integral approach, particularly, its equivalence to the 2nd-quantized approach, and its relation to Feynman diagrams.
- This book will drive the more mathematically inclined crazy, as the author admits, it makes very little attempt at rigour, and is very uncareful. He exchanges orders of limits willy-nilly, and often is not even clear about what sort of limiting process is taking place. There is not discussion of functional integration measures, or convergence, and there is very little justification provided for regularization methods (actually the coverage of dimensional regularization is extremely sparce, and would have been unfollowable, had I not already known it).
General Comments:
- I think that, contrary to some of the previous reviews, that the first few chapters of the book (through 6) would be a good first exposure to quantum field theory. I think the reader would have a much better understanding of the theory. However, the rest of the book is quite advanced, and would not be good for the uninitialized.
- I think that in an effort to make his coverage thorough and abstracting his discussion from phenomenology, the author sacrificed some of the readability of the book. That being said, if you're serious about learning the subject, this is a good resource.
Brilliant.......2006-09-15
Weinberg never disappoints the serious student of theoretical physics. There is no good reason to ignore perusing his texts.
Weinberg is a master expositor and creator of modern physics.
There simply is no good reason not to purchase his volumes.
superb book .......2006-08-16
in my opinion this should be one of the best books in qft.
Althought I've read jauch&rohrlich photons and electrons, p.ramond, itzykson, and ultimately, hatfield, Weinberg lead all of them for many heads. The features of this book are clarity, deepness, rigor, and authoritative treatment of all the topics. The discussion for a lagrangian versus hamiltonian formalism is lucid,and no finded in any other book. Group theory is applyied when is customary without cross over the physical implications. It contains a chapter devoted to scattering like no other book, wich is clear and explain concepts involved with "in" and "out" states(other of the lacks of many books of qft). Even the problems that contain are very well picked up, and solvable in most cases. I could't find any fault or mislead in what i read in this book, perhaps any skilled reader can find some. Even binding and typography are excellent, there is nothing more valuable for hardly 40$.
Reading for Rhetoric.......2006-03-31
Physics is usually a horribly taught subject, that is why most students avoid it. When it is effectively communicated, physics can be wonderful. This book represents the former. It is dense. The author is obviously a brilliant person; but, he is not a brilliant communicator. I've got a Master's in Physics and I was lost by the end of the second chapter. I have no doubt that the mathematics as presented are accurate; however, alone they fail to effectively communicate the substance of the topic to a mere mortal. Weinberg does not spend adequate time discussing the context, reality, or historical evolution of his ideas. I purchased all three volumes and, apparently, waisted my money.
I later purchased Roger Penrose's "The Road to Reality" and thoroughly enjoyed it. It was not an easy read either, but Penrose spent a significant amount of time recounting historical context, impact, and the 'reality' of his ideas.
Perfection, but advanced.......2006-01-10
This is one of the best written physics books to ever hit the market. However, it deals with an advanced topic and its not for the faint of heart or those without the proper background. Weinberg's writing style is remarkably clear. A historical introduction (which is very enlightening) is followed by a nice chapter on relatavistic quantum mechanics. Later chapters which I found very useful include a chapter titled "Quantum Fields and Antiparticles", where he introduces the Dirac formalism, and "The Feynman Rules", which is one of the best presentations on this topic I have come across. Chapters on the Lagrangian methods and path integrals are also good. I would strongly advise the reader to thoroughly study other quantum field theory books before tackling this one.
Also recommended (to get started): "Quantum Field Theory in a Nutshell"
Book Description
In this second volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly expoistion of quantum theory. Volume 2 provides an up-to-date and self-contained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Exercises are included at the end of each chapter.
Customer Reviews:
The most authoritative book on QFT ever.......2006-01-02
Before Weinberg's books, a typical graduate student in theoretical physics would study the standard textbooks (e.g. Itzykson-Zuber, Peskin-Schroeder) to pass QFT courses. When confronted with actual research problems, he would discover that all he has learned is how to do calculations in perturbation theory, that he is unfamiliar with a host of ideas and techniques that are widely used in the present-day research literature and that he has to resort to original papers and reviews to learn them.
Weinberg's three-volume set drastically changed this situation, giving the most authoritative and complete presentation of QFT to appear in a textbook. Although it is not suitable for beginning graduate students, it is invaluable for covering all these topics that are typically omitted in QFT courses and for providing valuable insight missing from other textbooks.
The highlight of the set is Volume 2, which includes most topics where Weinberg has made his own invaluable contributions. In his inimitable style, Weinberg guides us through the great developments in QFT from the 1960's to the 1980's, including most topics that are essential for a working knowledge of modern QFT. The presentation is crystal clear throughout and every topic is presented in as much detail as it deserves. In particular, the chapters on spontaneously broken symmetries are simply masterpieces, the treatment of anomalies is the most complete ever, while the chapter on extended objects is a thorough overview of an ever-expanding subject. This book is a must for everyone working on theoretical physics.
If you appreciate Vol 1, you'll want Vol 2. .......2005-03-26
I have found this text extremely useful as a guide to the essentials of modern renormalization theory, as well as modern quantization techniques for Non-abelian gauge theories. The chapter on extended field configurations is nice, though it is meant as an overview and guide to the literature. What I like most about this volume is the discussion of experimental or phenomenological issues that complements many of the discussions. He has a broad base of knowledge in particle physics, as well as field theory. If you don't have volume 1, get that first.
Delightfully insightful.......2002-12-23
This book has some of the most exquisite expositions on the theoretical aspects of quantum field theory that you are ever likely to run into, i.e. Weinberg's name is literally stamped on every page for brilliance. There are topics treated here that are not likely to be found anywhere else, for instance Batalin-Vilkovisky Quantization. Weinberg's treatment of the proof of renormalizability is compact and yet very readable. And his chapter on anomalies is simply speaking the authortiative treatment. This book is a must have for anyone interested in the more theoretical aspects of Field Theory. Though I would recommed a few months with Peskin & Schroeder, and volume 1 of Weinberg to get the full flavour of Weinberg's treatment.
Excellent, despite some idiosyncracies.......1999-01-22
This is another gem of a book by Weinberg. The discussion is fairly modern at places (for instance nice discussion of BRST, BV Formalism, RG and Anomalies), but could have been more modern and compact in certain other places (like chiral lagrangians, standard model etc.). However, even those parts are a pleasure to read. It is just that some other aspects could have been discussed (as I hope he does in the third volume), such as SUSY, especially QFT dualities. Anyway, an excellent book!
Book Description
This book is a modern introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the author develops the quantum theory of scalar and spinor fields, and then of gauge fields. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of "topological" objects in field theory and, new to this edition, a chapter devoted to supersymmetry. Graduate students in particle physics and high energy physics will benefit from this book.
Customer Reviews:
Good physical intuition into the topic.......2007-10-03
To understand quantum field theory it is necessary to read more than one author. Ryder's book should definitely be included in the list of titles.
Overview of QFT for those wanting a refreshing.......2006-12-06
This book should not be used for beginners by which I mean those individuals with a background in QM and SR but not QFT. It presumes, like any QFT text, a thorough understanding of QM and SR. A strong foundation in tensor analysis, group theory, differential geometry and lie groups is recommended.
It has some interesting ways of introducing topics in QFT for example the dirac equation:
The author begins by showing the defects in quantizing the energy mass relationship resulting in the Klein Gordon equation. The author digresses before introducing the dirac equation and goes on about the correspondence between SU(2) and O(3), rotation group in 3-D, and then introduces the correspondence between SL ( 2, C) and the Lorentz group. It is shown that the Lorentz group is essentially SU(2) x SU(2). Thus we can specify a state to be operated by a Lorentz transformation by two angular momenta. Special combinations of these give spinors which transform in specific ways under lorentz transforms. We see that the dirac equation is a relation between these spinors.
Symmetries of the Langrangian and the "appearance" of gauge fields in constraining the Langrangian to certain local symmetries from global ones is introduced almost immediately. We see how this necessitates the introduction of the electromagnetic field. Maxwell's and Proca's equations are put in tensorial form. There is a nice section here on the geometry of gauge fields. Differential geometry really helps here.
The canonical quantization of scalar, spinor and photon fields is undertaken.
Path Integral quantization of spinor scalar and gauge fields is undertaken. The usual topics of functional integration and wick's theorem are dealt with. With see how Zo(J) ..transition amplitude of particle creation and destruction with source..is the generating functional for free particle green functions and it's relation to n point functions and VEV is given.Interaction are introduced and their relation to Zo(J) is explained. The relation between greens functions and the S matrix are derived. It is shown how the usual approach for photons does not work requiring gauge fixing. Fenyman rules for all of these are derived.
Spontaneous Symmetry breaking and the standard model is briefly delved into. Renormalization is dealt with.
Overall, I found the presentation of the material disorganized with poor motivation for the topics. However, the derivations are detailed and a nice supplement to other QFT books.
One major drawback is the lack of problems.
ryder.......2006-02-28
its a good book for the beginners.The only drawback is it does not have exercise problems.
An Inspiring Introduction to QFT.......2002-10-01
One of the basic questions in the education of theoretical physics is, what is a good way of introducing QFT and giving the student a taste of what is to come? In my opinion, this book offers a fine solution to this thorny problem.
There are many sides to this question; for example, there is the view that the students should be exposed to this vast topic in a complete and thorough way (for such a text, I HIGHLY recommend Weinberg's 3 volume set, which, if not commonly regarded as a classic yet, soon will be), and also there is the point of view that most of the students studying QFT are experimentalists, so they should first be exposed to how to calculate amplitudes and cross sections for useful processes as soon as possible (see Peskin-Schroder for an outstanding exemplification of this principle). Both of these points of view have strong arguments supporting them, and there are many other reasonable opinions that might be taken; perhaps this is an indication that there is not any one approach to this subject which is a good introduction for all, but rather that the student must choose intelligently which text he/she finds they are most comfortable with. However, I can say that for me at least, this book had just the right selection of topics and at just the right level to get me interested in the subject and to give me a taste as to what it would be like if I were to go into it in more depth (which indeed I did). Other reviewers are quite right in pointing out that there are several inaccuracies in this text; also in more than a few places the treatment is considerably less clear than it might have been (this is one of the main strengths of Weinberg's set; every last detail is crystal clear, and the physical reasoning in the derivations is very rarely muddled in the math). Perhaps in this sense, the book could have been better written, and just by this element of style, I probably would have rated this 4 stars. However, I think that these valid criticisms are more than offset by the overwhelming strength of the book:that it is truly inspiring. Several reviewers have gone over details; I shall not rehash these matters, but instead leave off with the statement that this book was the best introduction to QFT that I could have bought.
one of good books.......2002-03-08
1)as other reviewers put, we cannot expect every thing from one source. but without doubt, this is a good buy.
2)this is not so pedagogic as the book seller's copy on the backcover. it needs some endeavor of course.
3)major flaw i noticed is only one: at page 150 the author mingled two different things i.e. (a)subsidiary condition which excludes unphysical state from consideration (b)re-definition of norm which brings the unphysical state into consideration.
Book Description
Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.
Customer Reviews:
Probably the best book on CFT.......2006-10-27
I have come across some books and lecture notes on CFT, but this book truly is great - almost all notes are based on this book. It presents elementary CFT at an understand pace and progresses slowly towards the end to the more advanced topics in 2D string theory and statistical physics.
The book is pleasant to read and the derivations are done well. Some minor errors and typos are forgiven, because the rest of the book makes well up for them. Numerous examples are given in each section and there are many problems at the end of each chapter. Unfortunately, there are no detailed solutions available, as far as I know.
Some prior knowledge of QFT might be useful, but the basics (Lagrangian formalism, Wick's theorem, Noether's theorem and conserved currents, etc.) are provided in the first chapters. This book is highly recommended for those interested in CFT and its application to string theory (and statistical physics), and I even dare to say it is a MUST!
This is a great book for beginners to learn CFT........1999-09-03
This book is really well done. It introduce the theory of conformal fields in a really pedagogical way so that any person not familiar at all with the subject can enjoy it. The review of quantum field theory and statistical mechanics at the begining is excellent and it is of great help if you haven't work with these subjects recently. The book is also filled with many basic applications that make the theory closer to real life.
Congratulations for this nice book!
A definite "must have" for those interested in CFT........1999-08-31
This book is a fine contribution to the literature on conformal field theory and will no doubt become one of the standard references on the subject. It is well worth the price as it gives a comprehensive introduction to the subject. Chapter 5 is a good discussion of local conformal invariance and clears up some of my own misunderstandings of this invariance. The later chapters discuss affine Lie algebras and algebraic considerations in detail.
Very complete, the reference in the field.......1999-04-27
Probably the best book to introduce you to conformal field theory. It starts from basics and go up to coset constrcutions, WZW models. More than a textbook, it is a necessary reference!
Book Description
Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This third volume of The Quantum Theory of Fields presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics that is likely to be at the center of future progress in the physics of elementary particles and gravitation. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, nonperturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, some of it published here for the first time. Problems are included.
Customer Reviews:
Defective Hard Cover.......2007-01-04
The whole current production run of this book has a defect. A glue is bleeding through on the inside of the hard cover fold, front and back. This does not seem to affect the structural quality of the book and is not visible from the outside. If you need this book and get it with this defect, don't bother trying to exchange it.
Once again, great book.......2005-03-26
Finding good introductions to supersymmetry can be difficult. Most introductions concentrate on N=1 supersymmetry in four dimensions, and there the superfield forumlation can be useful. However, when you go to N=2 supersymmetry (e.g. when considering theories in five or more dimensions), component fields can be better. Many times it's a matter of taste. For those cases, you have to go to review articles. Anyway, Weinberg concentrates on N=1 4D supersymmetry and supergravity using the superfield formalism. However, he ventures into the N=2 strong-weak coupling results of Seiberg and Witten, which are now a fundamental part of (supersymmetric) field theory. The text is, as the previous volumes are, a fantastic resource for learning the subject, and as a reference (for things like gravity- and gauge-mediated supersymmetry breaking, as well as the minimal supersymmetric standard model, which are open areas of reserach). As for all modern areas of research, the body of knowledge is stacked higher every year; but the topics covered here stand as solid fundamentals of supersymmetry. For more advanced topics, one is forced to go to the recent literature.
A self-contained treatment of the subject.......2000-04-20
If the two first volumes of "The Quantum Theory of Fields" were considered masterpieces in a modern and original presentation of the basics of quantum field theory and its penetration in the recent development of particle physics, with the machinery of spontaneously broken gauge theories, the new volume embraces the wide subject of supersymmetry in Weinberg's typical style, which always means a self-contained treatment of the subject, from its foundations and motivations, to its most recent application as a possible scenario for new physics beyond the Standard Model.
A complete review is published in CERN Courier, May 2000
Weinberg Keeps the level!.......2000-04-07
Great book, contains a lot of material, will be useful to many as a reference on supersymmetry for years to come. Highly Recommended!
Book Description
This book gives a comprehensive account of local quantum physics, understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach it describes both the physical concepts and the mathematical structures, and their consequences. These include the emergence of the particle picture, general collision theory covering the cases of massless particles and infraparticles, the analysis of possible charge structures and exchange symmetries, including braid group statistics. Thermal states of an unbounded medium and local equilibrium are discussed in detail. The author takes care both to describe the ideas and to give a critical assessment of future perspectives. The new edition contains numerous improvements and a new chapter concerning formalism and interpretation of quantum theory.
Customer Reviews:
I practically owe my today's academical self to this work..........2004-10-12
As someone working in the field created by Prof. Haag - Local Quantum Physics, aka Algebraic Quantum Field Theory - I feel somewhat oblidged to write a review on this book. This is all the more true when a large amount of misunderstandings about this subject among, so to speak, "outsiders", pervade the community of theoretical physics. As for me, I had the good luck of having Local Quantum Physics as my entering door to Quantum Field Theory, after my undergraduate involvement with Nuclear Physics. Learning this through (in a major part) Prof. Haag's book, alongside with a conventional course in QFT, has helped me clear several conceptual issues underlying QFT tools and calculations - specially renormalization - which alone seemed to me more witchcraft than physics.
The aims of Local Quantum Physics, even when linked to computational issues, are eminently structural and conceptual, going beyond particular models. These concerns are transparent in this book, where only the essentials of the Lagrangian approach are mentioned, and even these with a conceptually clean and deep purpose (just to cite an example, quantization of free fields are treated in a covariant way by using the Peierls' bracket, instead of canonical quantization), and with no predilection whatsoever by any particular quantization technique (for instance, path integrals are only mentioned "en passant", with no formulas, in Section VIII.1, in the discussion on the Euclidean/Lagrangian approach to QFT). This last proviso, which is a common source of complaint, actually (at least, it looks so to me) bears the following message under the aegis of the aims above: the physical concepts of QFT have nothing to do with the quantization method chosen. Although the justification for this is somewhat subtle, it ends up being a natural consequence of the line of thinking along which this book proceeds.
Most of the things about which Prof. Haag writes in this book seem to have been thought about for a pretty long time. It's thanks to this that the formalism of Local Quantum Physics acquired a remarkably flexible and synthetic language. The underlying idea, present in almost every topic treated in the book, is the principle of locality ("Nahwirkungsprinzip" = "Principle of local action", i.e., no action at a distance). Namely, that physical procedures are all localized in finitely extended regions of spacetime, as it "usually" happens in experimental situations, and that the matter of choosing a Hilbert space on which these procedures act (often based on global criteria such as the concept of a vacuum state) is mainly a matter of convenience. The abstract framework of C*- and von Neumann algebras is what allows one to work independently of a particular representation. This is strengthened by Einstein causality - physical procedures localized at causally disjoint regions commute with each other (This is quite distinct from locality in the sense of the EPR phenomenon, which is intrinsically linked to the notion - here generalized - of states, this one still highly nonlocal, as restrictions of a state to two causally disjoint local algebras of procedures can, and do, present quantum entanglement if this state is suitably prepared), and Poincaré covariance.
The principle of locality, when applied to the myriad of inequivalent representations of the local algebras which is characteristic of QFT, lead to enormous achievements (most of them described in the book), such as: the meaning of internal global symmetries and fermion degrees of freedom, and how these emerge from the observables alone, independently of the assumption of an underlying field theory (superselection sectors); the meaning of infinities and renormalization in perturbation theory (disjointness and quasi-equivalence of representations); a natural setting for QFT at finite temperature and its thermodynamics (KMS condition, modular techniques, phase space conditions); when moving to curved spacetime, the clarification of the (still open) issue of the choice of physical states from nonessentials and how this forces us to "unlearn" several concepts of Minkowski QFT (Unruh effect, etc.). Recent developments by the schools of Wald and Fredenhagen show the growing importance of the latter and related problems.
Finally, other two admirable aspects of Haag's book are the honest treatment of latest developments regarding conceptual open issues such as the meaning of local gauge invariance in quantum theory, the infrared problem, and questions regarding the interpretation of quantum mechanics and the meaning o spacetime itself. Haag's closing personal views on the latter, in the light of the mathematical formalism of Local Quantum Physics, bear an intriguing resemblance with modern ideas by Rovelli, Ashtekar, etc. on loop quantum gravity.
The book as a whole takes quite some time to digest, due to the mathematical machinery involved (functional analysis and an acquaintance in C*-algebra theory are a rather strongly recommended background) and the subtlety of the physical ideas. But, to sum up, for me it was, in due time, the ultimate temptress.
A complete recapitulation.......2002-04-26
LQFT, a kind of Axiomatic Quantum Field theory, was slowly
developed during the 1970 age to provide solid fundamentals
to quantum fields. Haag was one of the leaders of the
development, and this book resumes the climax of the theory.
From here the development has continued, looking for nets
of observables as a tool to incorporate the renormalization
mechanism. But it is to be noted that, since then, a branch
of C* algebras has developed to formulate NonCommutative
geometry, a tool completely unavailable to the people working
in Local Quantum Field Theory. One should kept a leg in
each side, aiming to marry both formalims.
Deserves 10 stars.......2002-04-16
Quantum field theory is a subject that has occupied the time of an enormous number of researchers, both in physics and in mathematics. Those who have studied perturbation methods in quantum field theory have no doubt run acroos "Haag's theorem" that is usually loosely stated as saying that "the interactive representation does not exist". The statement of this theorem, and many other results in quantum field theory, particularly the procedure of renormalization, have been viewed by many as unsound from a mathematical standpoint, and so efforts were begun to put quantum field theory on a rigorous mathematical foundation. Going by the names of axiomatic or constructive quantum field theory, these approaches are interesting, but also a little troubling from a scientific perspective. Axiomitization is usually appropriate in mathematics when a subject has matured to the point where it can be "closed off", and this usually happens when the theory is very well understood and so its essence can be codified in a few well-forumlated axioms. But quantum field theory is no where near that stage; indeed one can say that it continues to be a theory that, oddly, has immense predictive power but whose rigorous mathematical formulation remains elusive. Not only that, quantum field theory is still in a course of evolution, and any attempt at axiomitization might become obsolete as soon as it is put down on paper. In addition, physical insight, as much as mathematical understanding, must not be sacrificed in any resulting axiomatization of quantum field theory. Frequently, the result of axiomatization is to divorce a physical theory from its physical roots, and beginning students of the theory then have difficulty in acquiring intuition of the essential physics of the theory.
One of the best attributes of this book is that the author realizes this, and early on he refers to "general", rather than "axiomatic" QFT as being more appropriate since it allows flexibility in relation to future discoveries. Not only that, the author endeavors to explain the formalism that he is expousing in the book, and he succeeds brilliantly. Anyone interested in the mathematical physics behind quantum field theory, and not just doing bread-and-butter perturbation calculations, will gain a lot from the reading of this book. It is packed full of insight, a rare occurence in books that employ the heavy mathematical formalism that this one does. One will need a strong background in operator theory, abstract theory, and several complex variables to read the book, but a lot of this is developed impromptu as the text unfolds. When it is not, the author gives references for those readers who need more in-depth discussion.
There are so many ineresting discussions in this book that space does not permit an evaluation of all of them, but the following is a short list of points in the book that I found particularly well-written: 1. The Wigner analysis of irreducible unitary representations of the Poincare group. This is not a mathematically rigorous discussion, but the author points out the physical relevance of the fact that the spectrum of the 4-momentum operator must be concentrated on a single orbit. This fact ensures the stability of matter. And, as frequently happens in physics, several mathematical consequences of a particular physical theory are discarded as not being relevant; in this case the other three classes of the irreducible representations. That being said, the author does include as of possible physical relevance the idea of parastatistics. He points out his reasons for this, namely that a strict adherence to the Bose-Fermi alternative is not operationally justified. 2. The role of fields in implementing the principle of locality and not as observable particles. This fact is usually not emphasized in books on quantum field theory. 3. The author clarifies the distinction between the notion of locality that deals with the commutation of two observables that are space-like separated, and the one dealing with the Einstein-Podolsky-Rosen paradox and Bell's inequality. 4. The discussion on the Bose-Einstein alternative, in particular the suggestion that parastatistics can be replaced by Bose or Fermi statistics in the presence of a non-Abelian unbroken global gauge group. 5. The discussion on topological charges and their prohibition by the Doplicher-Haag-Roberts selection criterion. The Doplicher-Haag-Roberts criterion was used in scattering theory and thought to be reasonable, but the author shows that its use is problematic in this case also, as well as in prohibiting topological charge. Purely massive fields can, it turns out, have measurable correlations at large distances, and Borcher's selection criterion, also discussed along these lines, gives topological charges. 6. The treatment of the Tomita-Takesaki theorem, modular automorphisms, and their connection to the KMS-condition. 7. The discussion on the need for type III-1 von Neumann algebras in relativistic quantum field theory versus type I in ordinary quantum mechanics. Such a von Neumann algebra is hyperfinite and is unique. 8. The discussion on the impossibility of coherent wave packets of one-electron states in quantum field theory, as contrasted with the usual practice in quantum mechanics. This is dues to superselection rules and the "infraparticle" nature of electrically charged particles, which are not associated with discrete eigenvalues of the mass operator. The author asks the reader to justify electron interference experiments in quantum field theory.
The most important book about algebraic qft by its founder.......1999-05-01
In spite of the succes of quantum field theory it became very early clear that this theory needed a new mathematical formulation. Haag was one of the founders of this new theory which was later called algebraic quantum field theory but Haag himself preferred "local quantum physics".
The algebra of observables is designed as the C*-inductive limit of a net of von Neumann-algebras the index set of which is formed of open subsets of space-time. The book discusses the DHR-selection criterion as well as the BF-criterion of Buchholz and Fredenhagen that is more adequate to massive fields. Furthermore Haag gives a short introduction to statistical qft in the algebraic framework. Especially the KMS-condition which was formulated in the sixties by Haag, Hugenholtz and Winnink is discussed.
A highly recommended book!
Book Description
The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.
Customer Reviews:
Much inferior to Ryder for intro QFT.......2002-06-09
I endorse most of what the reviewer below says except that Jasonc65 from Wilmington has forgotten that the derivative with respect to complex z=x+iy is d/dz=1/2(d/dx - i.d/dy) so that he should have got pi=half[i.phi(star)] by both methods - which is the right answer! Hatfield has simply got it wrong. Similarly,pi(star)=minus half(i.phi). For the correct treatment see Franz Gross "Relativistic Q.M. and Field Theory" chapter 7. And it's not the only error; simply "plugging (2.52) into an equation like (2.47)" clearly does not give (2.50) and (2.51) but gives an imaginary probability density and no i-factor in the spatial components.
Hatfield's treatment is not the step by step approach claimed but rather piecemeal and with a cavalier attitude to index house-keeping minus signs and factors of i and 1/2 etc. He is further let down by the typesetting of Perseus books that makes hardly any use of boldface characters, uses a point size for indices and suffixes not much smaller than the normal font and an almost typewriter-like character spacing in equations and formulae that make them sprawl across the page in a way less easy to scan than most other publisher's neatly grouped expressions.
For a step by step introduction that is clear, reasonably rigorous and more readable than Hatfield, I would strongly recommend Lewis Ryder's QFT book notwithstanding that it is mainly oriented towards the path integral formulation.
an intriguing book, what should I say?.......2002-04-03
This book promises to be a nice read for someone with minimal background. And many people with backgrounds in physics say it's an easy read. Maybe it is for them, but not for me. Now, I admit, I am a wannabe physicist. Most of my background is in pure mathematics and computer programming. However, I have recently taken up an interest in physics, and of all the sciences, I find that books in advanced physics are the most difficult to understand, in general. It has taken me many painful hours just to understand the Langrangian and the Hamiltonian, and just last week I finally mastered Noether's theorem. And by page 20 of this book, I'm exposed to the Lagrangian density, kind of a continuous extension of the notion of the Lagrangian. Well, generalizing from finitely many particles to a continuous field is not really that difficult. And I guess that is a very important insight in and of itself. But as I read the next 5 pages, I am absolutely dumbfounded by the stretch of rigor. I can't guess what rule they'll break next, as they assume that every calculation rule will carry over in their transition from one domain to another. In fact, as I write this review, I am still stuck pondering page 25, wondering how they justify every single step.
This is not the first time I've tried to read this book. I've had to frequently consult other books on mathematical physics before I could proceed any further. Now, I admit, that while my background in mathematics is thorough, I've never had a formal education in physics, and I'm trying as best as I can to read all the books on mathematical physics, quantum mechanics, QFT, QED, GR, etc. And I think I have the handle on the Hamiltonian, and how it is used in both classical and quantum mechanics.
On pages 21-22, I have to pour over calucations using integration by parts, and using some unstated boundary conditions, a minor difficulty with which I can cope. But then I find out the the author wants the Lagrangian density to depend on a complex function, and it's conjugate. So while I'm stuck in the middle of page 23, I have to redo all the calculations in my head. Now, that sure isn't step by step detail, as the preface claims. The author doesn't even tell me how I'm supposed to differentiate with respect to the complex functions. Am I supposed to treat the field and its conjugate as complex variables, or am I supposed to pretend that the Lagrangian density really depends on the real and imaginary parts of the field and thus consider two real fields instead of one complex field? I've tried both methods, and neither one of them satisfies my sense of rigor.
In equation (2.52), the author gives the Lagrangian, promising the reader it can easily be calculated by working backwards through the previous equations. I don't find that easy to do in my head at all. I've managed to work forwards and verify that the Lagrangian satisfies the invariance and reproduces Shroedinger's equation. But that was only after I poured over the next paragraph and realized that the transformation factor was supposed to be an imaginary number. Until then, it didn't make sense at all.
Now, I get to (2.53), where Hatfield gives the conjugate momentum as pi = i conjugate phi, without showing any intermediate steps. I tried differentiating with respect to the real and imaginary parts, and I got pi = -i phi. When I tried it again with complex differentiation, which I feel is less plausible, I got pi = i/2 conjugate phi. As always, either I'm not understanding what how the author wants me to make the transition, or else he's doing a sloppy job of it. Of course, like most other physics books, there are arithmetic errors that I have to sort through, and that only makes it worse. I find out only after pondering for days on a single line that the author meant a plus sign where he used a minus.
Well, I tried to forget about this confusion and move on. The author gives the Hamiltonian in (2.55), and then begins to discuss how to second quantize the result. Now, I'm not even sure how the differential operator carries over. In order to justify the claim that (2.55) reproduces the (2.37), it seems that I have to now assume that both d/dx and V(x) commute with phi(x,t). In the first quantized system, this is pure nonsense.
Now, I'm on page 25, where the author is discussing expansion in terms of eigenfunctions. It is smooth sailing until I get to (2.59), where in order to justify the last step, Hatfield makes the absurd claim (2.60), and I'm still trying to figure it out. I can only justify that claim if I confuse integer variables with continuous variables and treat the equation as a matrix equation. After all, you're dealing with a unitary matrix. But just try it with Hermite functions (energy eigenfunctions for the harmonic oscillator problem) and you'll run into problems with infinities. Of course, calculations with the Dirac delta function have never been fully rigorous, so maybe I'm kidding myself.
As you can see, I've only begun the book, so I can't really give a complete review of the whole thing, but it sure seems to be promising to be one headache after another.
Nice to read, but not complete........2001-03-20
This book is nice to read, I agree with most of the previous reviews about this. Some things are interesting, e.g. the chapter on Schrodinger picture, which is almost completely ignored in most textbooks. The style is very readable and the text gives some useful insights. However, it is not suitable as a reference on QFT or on strings because a number of subjects are left out: renormalisation of gauge theories (only QED is handled), symmetry breaking, the standard model, dimensional regularisation, supersymmetry, superstrings. In less pages, Ryder covers all these subjects, except strings, but in the end gives less insight on the inner working of the theory.
One of the best for understanding QFT.......2001-03-14
This book is readable (you don't have to sit down with paper and pencil and work out a page of calculations to get from one line to the next, for most of the text)and it is clear (concepts are defined and explained). It is not really suitable as a first exposure to QFT for the reader would be better off with some familiarity with Feynman diagrams and relativistic quantum mechanics beforehand. With this background Hatfield's book is very valuable as a source for understanding the meaning behind QFT. Many other field theory texts seem to be concerned with little beyond the motions of handling the mechanical formalism and obtaining quantitative results to problems. This book instead gives the reader insight into field theory, does a good job at giving the big picture and stressing the transition from ordinary QM to the field aspect. Besides this, Hatfield's informal prose makes the book enjoyable to read. It has a fair share of typos throughout but most are quite easy to find. Compared to some of the popular field theory texts out there (P&S, Ryder) this one stands head and shoulders above.
Excellent reference book for students.......2001-03-07
This is not a typical field theory book. From the very beginning the aim is to teach the reader all the concepts and methods which will be useful to learn string theory which form the last third of the book. Excellent examples of this can be found in the chapters on path integral and also in the chapter on Fadeev-Popov method. Almost all calculations are shown in step by step detail and it is very useful for the students who are learning field theory for the first time. The organization of the book is a little different from the usual mold of field theory books, but one can get use to it. One just has to realize that while most of the field theory books on the market (except for Weinberg's 3 volume text and one or two other) aim at teaching how to derive Feynman rules and how to calculate a few processes , this book by Hatfield is trying to take the "field theory book" audiance (who are usually phenomenology oriented) to a different playground "introduction to strings". This is an excellent book and a definite break from the old "B&D book 1 and 2" tradition and I would recommend it to both students and teachers (most of whom are still stuck in the old mode) alike. K. M. Maung Department of Physics Hampton University Hampton, Virginia 23668
Book Description
Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises.
Customer Reviews:
Excellent.......2001-11-01
This book is very nice. Not only does it present the theory and give problems, the problems are solved in the appendix (for the most part) and many references are cited, allowing the reader to review work elsewhere. If you are interested in quantum fields and gauge theory, I would suggest reading and working out of this book.
Book Description
This text introduces the theoretical framework for describing the quark-gluon plasma, an important new state of matter. The first part of the book is a self-contained introduction to relativistic thermal field theory. Topics include the path integral approach, the real and imaginary time formalisms, fermion fields and gauge fields at finite temperature. The author illustrates useful techniques such as the evaluation of frequency sums and the use of cutting rules. The second part of the book is devoted to recent developments, and gives a detailed account of collective excitations (bosonic and fermionic), showing how they give rise to energy scales that imply a reorganization of perturbation theory. The author also explains the relation with kinetic theory. He works out in detail applications to processes that occur in heavy ion collisions and in astrophysics. Each chapter ends with exercises and a guide to the literature. Graduate students and researchers in nuclear, particle, and astrophysics will benefit from this book.
Book Description
The book gives an introduction to the concepts and methods of many-body problems and quantum fields for graduate students and researchers. The formalism is developed in close conjunction with the description of a number of physical systems: cohesion and dielectric properties of the electron gas, superconductivity, superfluidity, nuclear matter and nucleon pairing, matter and radiation, interaction of fields by particle exchange and mass generation. Emphasis is put on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas in different domains of physics. The exposition is self-contained and displays in a coherent way all details of derivations starting from a basic knowledge of quantum mechanics and classical electromagnetism.
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General
| Science
| Subjects
| Books
The Quantum Theory of Fields, Volume 2: Modern Applications
The Quantum Theory of Fields
An Introduction to Quantum Field Theory (Frontiers in Physics)
String Theory, Vol. 1 (Cambridge Monographs on Mathematical Physics)
String Theory, Vol. 2 (Cambridge Monographs on Mathematical Physics)
