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Cambridge University Press eBooks

The ineliminable classical face of quantum field theory

Paul Teller

Published Feb 18, 1999• 4 citations
Publisher

Abstract

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’.

DOI
10.1017/cbo9780511470813.026

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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’.
It is very likely that most readers and authors of articles appearing in Classical and Quantum Gravity are interested in what might loosely be termed the philosophy of science. It is equally likely, with perhaps a few exceptions, that the research of these same readers and authors has not been influenced in the least by the work of professional philosophers of science. This is certainly the case for those of us who work in quantum field theory. One must therefore ask who the intended audience is for a book which purports to discuss the philosophical implications of quantum field theory. In the preface, the author states that there are two intended audiences for his book. The first is `other interested interpreters of physics' who wish to learn something about quantum field theory in as painless a way as possible. The second is for students of physics who are bogged down in the details of learning quantum field theory and cannot see the overall picture. I am not convinced that either audience will find this book to be of much use. There are two basic problems with this book. The first is that the quantum field theory in it is of the old-fashioned kind, and is not really representative of the way the subject is either taught or thought of today. The second is that there is not sufficient background material present to make this book suitable for a novice reader. For example, I wonder how much a reader who has not studied quantum mechanics in any depth will get out of a treatment which launches into Hilbert space and a discussion of states without much in the way of proper introduction. Any reader who is familiar with the workings of quantum field theory will find much to disagree with in this book. For example, the author tries to make a case that a Fock space description is better than talking about particle labels and restricting to symmetric or antisymmetric states. The reason claimed for this is that there are states in Fock space which are neither symmetric nor antisymmetric under particle interchange which must be discarded. (In the author's words, this introduces `surplus formal structure'.) However, in Fock space an equally arbitrary choice is made by focusing on relations among the creation and annihilation operators which involve only commutation or anticommutation relations. Although this is acknowledged by Teller, no satisfactory explanation is given as to why one procedure is any less arbitrary than the other. The book is incomplete in many ways, with many interesting points mentioned just in passing. For example, the discussion around the Newton--Wigner position operator would have been greatly enhanced by including more details, such as an explanation as to why quanta described by Newton--Wigner states seem to propagate at superluminal speeds. It is hard to believe that a reader who has not met the Rindler vacuum before would find Teller's discussion to be very informative. After being so critical of this book, I should mention a part which I did enjoy and would recommend to students of physics. This is the last chapter of the book which contains a discussion of renormalization theory. It is my experience that students often find renormalization theory confusing, and may find Teller's semiqualitative discussion illuminating.
Introduction: Conceptual issues in quantum field theory Part I. Philosophers' Interests in Quantum Field Theory: 1. Why are we philosophers interested in quantum field theory 2. Quantum field theory and the philosopher Part II. Three Approaches to the Foundations of Quantum Field Theory: 3. The usefulness of a general theory of quantized fields 4. Effective field theory in condensed matter physics 5. The triumph and limitations of quantum field theory 6. Comments Discussions Part III. Does Quantum Field Theory Need a Foundation: 7. Does quantum field theory need a foundation? Part IV. Mathematics, Statistical Mechanics and Quantum Field Theory: 8. Renormalization group theory: its basis and formulation in statistical physics 9. Where does quantum field theory fit into the big picture? 10. The unreasonable effectiveness of quantum field theory 11. Comment: the quantum field theory of physics and of mathematics Part V. Quantum Field Theory and Spacetime: Introduction 12. Quantum field theory and spacetime: formalism and reality 13. Quantum field theory of geometry 14. 'Localization' in quantum field theory: how much of QFT is compatible with what we know about spacetime 15. Comments VI. 16. What is quantum field theory and what did we think it was? 17. Comments Discussions Part VII.Renormalization Group: 18. What is fundamental physics? A renormalization group perspective 19. Renormalization group: an interesting yet puzzling idea Part VIII. Non-Abelian Gauge Theory: 20. Gauge fields, gravity and Bohm's theory 21. Is the Aharonov-Bohm effect local? Discussions Part IX. The Ontology of Particles or Fields: 22. The ineliminable classical face of quantum field theory 23. The logic of quanta 24. Do Feynman diagrams endorse a particle ontology? 25. On the ontology of QFT Part X. Panel Discussion.
The methods of quantum field theory underpin many conceptual advances in contemporary condensed matter physics and neighbouring fields. This book provides a praxis-oriented and pedagogical introduction to quantum field theory in many-particle physics, emphasizing the application of theory to real physical systems. This third edition is organized into two parts: the first half of the text presents a streamlined introduction, elevating readers to a level where they can engage with contemporary research literature, from the introduction of many-body techniques and functional integration to renormalization group methods, and the second half addresses a range of advanced topics including modern aspects of gauge theory, topological and relativistic quantum matter, and condensed matter physics out of thermal equilibrium. At all stages, the text seeks a balance between methodological aspects of quantum field theory and practical applications. Extended problems with worked solutions provide a bridge between formal theory and a research-oriented approach.
Introduction Chapter 1 dealt with one of the deepest mysteries in modern science: how to explain consciousness. This Part deals with another mystery: how to make sense of quantum mechanics. Both involve a problem of reconciliation with the classical worldview, which is one hint that the two mysteries might be related. A second is that, unlike classical physics, which makes no reference to or allowance for consciousness, quantum theory raises the issue of consciousness and its relationship to the physical world in a very direct way. These hints do not necessarily mean there is a connection between the two mysteries, but by the end of this Part I hope to have shown why it would be natural to look for one. My more immediate aim here is to give the social scientific reader an introductory understanding of the experimental findings of quantum theory, its key concepts, and the debates about its interpretation. The discussion assumes no prior knowledge of quantum physics and makes no use of mathematics. Quantum theory without equations might seem like an oxymoron, and certainly reading this Part will not enable anyone to use quantum theory. But to a perhaps surprising degree it is possible to understand quantum theory without being able to use it. Its findings can be communicated in ordinary language, and the same goes for its main concepts and interpretive debates. One consequence of this has been the emergence of a virtual cottage industry of books on quantum theory for a lay audience. Most are written by physicists, and many are quite good. However, it is not just popular treatments that do without equations: much of the professional philosophical literature does as well. (I draw on both kinds of literature below.) Philosophers of physics are trained to understand the math, of course, which is necessary for a full appreciation of the issues.
Approaches to Ontology: Candidate General Ontologies for Situating Quantum Field (P Simons) 'Quanta', Tropes, or Processes: Ontologies for QFT Beyond the Myth of Substance (J Seibt) Analytical Ontologists in Action: A Comment on Seibt and Simons (M Kuhlmann) How Do Field Theories Refer to Entities in a Field? (S Y Auyang) Field Ontologies for QFT: A Naive View of the Quantum Field (A Wayne) Comments on Paul Teller's Book, An Interpretive Introduction to Quantum Field Theory (G Fleming) So What Is the Quantum Field? (P Teller) Relativity, Measurement and Renormalization: On the Nature of Measurement Records in Relativistic Quantum Field (J A Barrett) No Place for Particles in Relativistic Quantum Theories? (H Halvorson & R Clifton) Events and Covariance in the Interpretation of Quantum Field (D Dieks) Measurement and Ontology: What Kind of Evidence Can We Have for Quantum Fields? (B Falkenburg) Renormalization and the Disunity of Science (N Huggett) Gauge Symmetries and the Vacuum: The Interpretation of Gauge Symmetry (M Redhead) Comment on Redhead: The Interpretation of Gauge Symmetry (M Drieschner et al.) Is the Zero-Point Energy Real? (S Saunders) Two Comments on the Vacuum in Algebraic Quantum Field (M Redei).
Abstract Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamic (QED) has been the first example of a quantum field theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. In fact, as hopefully this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, although excellent textbooks about QFT had already been published, I thought, many years ago, that it might not be completely worthless to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group (RG) properties are systematically discussed. The notion of effective field theory (EFT) and the emergence of renormalizable theories are described. The consequences for fine-tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised.