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An interpretive introduction to quantum field theory. (English) Zbl 0864.00019

Princeton, NJ: Princeton University Press. x, 176 p. (1995).
This book offers an introduction both to the interpretation and to the formal foundations of the theory.
The interpretive theme is that the wave/particle duality can be understood only if we ‘disassemble’ the notion of particle, arriving at the notion of quanta which have discreteness and a high degree of localizability, but do not have exact trajectories, or the ‘primitive thisness’ which allows one to be distinguished from another. States are interpreted as ‘propensities’ to manifest values, as are superpositions of states. The central thesis of the book is that this interpretive analysis also applies to quantum field theory: ‘The name Quantum Field Theory leads us to expect a theory that must primarily be thought of as a field theory. The single most important point I hope to make in this book is that this impression is wrong’ (p. 9). And later: ‘Armed with a clarified notion of quanta, and aided by my specification of how to understand superpositions, I will show that we are describing exactly the same facts when the description runs in terms of “quanta” and when it runs in terms of “fields”.’ (p. 10)
Although the main theme is interpretive this is in fact a highly formal book. It is a weakness that the interpretative discussion of Chapter 2 gives way suddenly to very formal presentations and both the style and the expertise assumed of the reader changes drastically at this stage, probably betraying the origin of some chapters as stand-alone papers designed for a different readership. However this is also a strength of the book in that key interpretive issues are clearly expressed and are explicitly related to the formalism. Thus Chapter 3 includes an analysis of aggregate systems, arguing that Fock space (a direct product of Hilbert spaces) is more appropriate than the usual tensor product space as a description of aggregable quanta. In Chapter 4 Fock space is re-expressed in a way that allows a field theoretic representation, i.e. in a form where operators are attributed to space-time points and there is a useful discussion here of what exactly is meant by a field theory. Chapters 5 and 6 continue the examination of field theoretic issues including the implication of relativistic concepts, and the book ends with a discussion of quantum interactions, Feynman diagrams and renormalisation, all within the author’s overall interpretation of quantum field theory.
The author himself admits at one stage that the wave/particle duality is perhaps not so much solved by his analysis as ‘transcended’ by it, and indeed the usual concept of a particle is so altered in the notion of quanta, that in one sense the interpretive issue may simply have been sidestepped. But the discussion is informative and has an unusual mix of lively discussion with formal rigour, producing an interesting book which extends the usual debate about quantum mechanics, lays a clear formal framework for discussions of field theory, and is thoroughly recommended.

MSC:

00A79 Physics
81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
46N50 Applications of functional analysis in quantum physics
81T05 Axiomatic quantum field theory; operator algebras
46C15 Characterizations of Hilbert spaces
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