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Title: An Interpretive Introduction to Quantum Field Theory by Paul Teller ISBN: 0-691-01627-5 Publisher: Princeton Univ Pr Pub. Date: 17 January, 1997 Format: Paperback Volumes: 1 List Price(USD): $20.95 |
Average Customer Rating: 3 (3 reviews)
Rating: 3
Summary: A fair introduction, but needs to be greatly expanded
Comment: Philosophical debate on quantum mechanics was very intense and widespread in the twentieth century, and it continues without abatement in the twenty-first. Philosophical issues in quantum field theory (QFT) however are not as common, this being due possibly to the level of physics and mathematics needed to master the subject. This book is one of the few that has appeared that deal with these issues, and it serves as a fairly good introduction to them.
In the preface, the author describes quantum field as a subject that is "notoriously hard to learn". He admits having severe difficulty in the learning of it, which he blames on the lack of good presentations of the subject. One can easily find though superb explanations of QFT in the literature, both in preprint and textbook form. His presentation of QFT could loosely be described as the "older" quantum field theory, since he does not address guage theories and makes no use of modern mathematical formalism. By his own admission, all of the ideas in the book were known by 1950.
The title of the book reflects the author's view of an interpretation of a theory, namely that it gives a similarity relation that is hypothesize to hold between a model and the properties of things that the model is supposed to characterize. This notion of similarity is a purely qualitative one though, as is typical in most discourses on philosophy. For the author, the issue for interpretation is the phenomenon of "superposition" in QFT, and he also endeavors to show that the "particle" intepretation of QFT is at equal level with the "field" theoretic one. He believes that current views on QFT get the particle aspect wrong, nor show how the particle and field aspects fit together. It is the particle labeling he says, that causes problems, and his solution is via the Fock space formalism, which avoids what he calls the "surplus structure" of conventional quantum mechanics, and which avoids the temptation to ascribe properties to particles. Instead he uses a conception of "quanta", which gives information only on what patterns of properties are exhibited. The Fock space basis states, and consequently the operators are indexed by space-time points, entailing naturally an interpretation of the theory in terms of fields. However, the notion of "operator-valued fields" that is typically expoused by practioners is criticized by the author and he lays out a different interpretation (but again using the Fock formalism), using as examples coherent states and vacuum fluctuations. He recognizes, quite correctly, that an interpretation as a quantum field takes place in a loose analogical relation to classical physics.
No treatment of quantum field theory could be complete without including a discussion of renormalization. The author does not really add anything new in his discussion, as a reader can gain essentially the same content and insight (and more) in currrent papers, preprints, monographs, and textbooks on the subject. The use of cut-offs and dimensional regularization are briefly discussed, but no new insights are given into them. His solution to the problem of renormalization is what he calls a "mask-of-ignorance" approach, in which he asserts that a correct quantum field theory will be completely free of infinities. The correct theory is unknown, but this does not matter as long as attention is restricted to expressions that are independent of the cutoff and the regularization scheme. This has been said many times already though, by many different researchers and expositors of quantum field theory. A quantum field theory free from divergences has yet to be found, but another approach to the problem of infinities has taken over, that one going by the name of string theory.
Rating: 2
Summary: a stepping stone, not a place to stop
Comment: My first exposure to QFT was Sunny Auyang's "How is Quantum Field Theory Possible?" I had hoped to find more details about the theory itself to supplement the parts of Auyang's presentation that I found difficult. I was disappointed to find Teller presenting QFT as it was in the 1960s, forty years ago, in contrast to Auyang's much more modern approach.
Five facts about QFT were brought home to me by Teller's book. (1) QFT is a metatheory, not a theory. It doesn't become a theory until critical parts are filled in by an actual model such as the Standard Model of particle physics. Teller gives no clue about how this works. (2) QFT is incomplete in many ways beyond its absence of gravity. (3) QFT is inconsistent, giving different answers to the same problem depending on what methods you use to solve it. Choosing the correct method is a key talent physicists must acquire. (4) QFT is sometimes very sound, giving extraordinarily accurate answers. These problems are all captured by observing that (5) QFT (at least as presented by Teller) is not rigorous; it's a toolkit of formalisms and techniques that have been developed with a perspective much more like engineering than like mathematics.
Teller's target audience is physicists who are able to treat nonrelativistic quantum mechanics and its interpretive problems as uninteresting background, and who want to know a little bit about some of the additonal interpretive issues that caused trouble during the development of QFT. If you want to know how those issues relate to the classic problems of philosophy, you need to go elsewhere. Auyang is a good place to start, providing significantly more sophistication in both philosophy and mathematics.
Rating: 4
Summary: Paperbound edition recommended for those new to the subject
Comment: I should say first that I write as a mathematician who is not a physicist, but who is interested in the subject. For readers with some knowledge of nonrelativistic, single particle quantum mechanics, this is a good place to get an idea of what quantum field theory is about. The opening chapters are more philosophical than the later ones, which are more mathematical, but one should be willing to consider the topic from both these angles in order to get the most from this book. The development of the occupation-number formalism and Fock space is very clear and enjoyable, but matters get more difficult later on. The occasional excursions into relativistic field theory frankly lost me a couple of times. The last chapter, on renormalization, however, is again very lucid and accessible to someone with even a modest background. It seems to me that much of the interpretive work Teller undertakes is to understand the relationship and possible differences between quantum field-theory -- i.e., QFT as quantization of classical fields -- and quantum-field theory -- i.e., a field theory of 'quanta' which lack radical individuation, or as Teller says, "primitive thisness." Along these lines he gives some very good cautions against interpreting Feynman diagrams literally. Since the work is highly introductory in nature, being much less technical and extensive than books of similar titles by Sterman, Kaku, et al., it seems a little expensive at its full $35 hardcover price, but is certainly worth the $16.95 asked for paperbound
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