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An Interpretive Introduction to Quantum Field Theory (Teller 1995; hereafter IIQFT) supersedes most of my prior work on quantum field theory. The gossip mill has described this book as a popularization of the most elementary parts of Bjorken and Drell (1965), which into the 1980s was the most widely used quantum field theory text. As with any good caricature, there is a great deal of truth in this comparison. Like Bjorken and Drell, who published in 1965, IIQFT presents the theory largely as it existed in the 1950s. But in order to see aspects of structure and interpretation more clearly, IIQFT presents the theory stripped of all the details needed for application. IIQFT also does not treat contemporary methods, such as the functional approach, and important recent developments, especially gauge theories and the renormalization group. Nonetheless it is hoped that by laying out the structure of the theory's original form in the 1950s, much of which survives in contemporary versions, and by developing a range of ways of thinking about that theory physically, one does essential ground work for a thorough understanding of what we have today.
Why do we use the term ‘quantum field theory’? A good fraction of the work done in IIQFT aims to clarify the appropriateness, accurate development, and limitations of the application of the epithet ‘field’, as well as examination of alternatives. While called a ‘field theory’, quantum field theory (QFT) is also taken to be our most basic theory of ‘elementary particles’.
Professor Murray Gell-Mann told us how, in 1963, in a submission to Physics Letters, he “employed the term ‘mathematical’ for quarks that would not emerge singly and ‘real’ for quarks that would.” Three years later he offered an improved “characterization of mathematical quarks by describing them in terms of the limit of an infinite potential, essentially the way confinement is regarded today. Thus what I meant by ‘mathematical’ for quarks is what is now generally thought to be both true and predicted by QCD.” But in using the term “mathematical” Professor Gell-Mann got himself into some hot water, for “up to the present, numerous authors keep stating or implying that when I wrote that quarks were likely to be ‘mathematical’ and unlikely to be ‘real,’ I meant that they somehow weren't there. Of course, I meant nothing of the kind.”
How did Gell-Mann get himself into this little predicament? “I did not want to call [confined] quarks ‘real’ because I wanted to avoid painful arguments with philosophers about the reality of permanently confined objects. In view of the widespread misunderstanding of my carefully explained notation, I should probably have ignored the philosopher problem and used different words.”
At the conference Gell-Mann told us about the doctor's prescription he kept posted in his office admonishing him not to debate philosophers, suggesting that his choice of the word “mathematical” was his effort to follow the prescription.