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Philosophical Foundations of Quantum Field Theory

Nick Huggett

Published May 1, 2003• 2 citations
Publisher

Abstract

Abstract Much attention has been directed to the philosophical implications of quantum field theory (QFT) in recent years; this paper attempts a survey in low-technical terms. First the relations of QFT to other kinds of theory, classical and quantum, particle and field, are discussed. Then various formulations of QFT are introduced, along with related interpretations. Finally a review is made of some of the most interesting foundational problems. For our discussion of the foundations of quantum field theory (QFT) it will be useful to have a map showing where QFT stands in relation to other physical theories. Figure 1 locates theories as points of a three-dimensional lattice: describing particles or fields, formulated in different spacetimes and either classical or quantum. Consider the classical plane of Figure

DOI
10.1093/oso/9780199250547.003.0012

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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.
Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual system for physical descriptions, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated; no discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest. Here, by basic ontology I mean the irreducible entities that QFT is invented to describe. The often mentioned candidates for the basic ontology of QFT, in fact of the physical world, are the discrete particle and the continuous field. Another possible candidate (the spacetime point) has also been suggested recently (Redhead, 1983). Since the aim of this chapter is to analyze the historical process in which the conceptual foundations of QFT were laid down, rather than the logical structure of QFT which philosophers of the present day treat, no discussion of the last possibility will be given. The content of this chapter involves the formation and interpretation, in a roughly chronological order, of the concepts of the wave function, quantization, quantization of the field, the vacuum, interactions between fields, and renormalization. The first two topics will be discussed in relation to the quantization of the field, with their role being taken as the starting point of the conceptual development of QFT.
Abstract The aim of this volume of essays is to delineate and examine a range of topics which represent a systematic account of the nature and implications of QFT. The contributors, who include Michael Redhead, James T. Cushing, Paul Teller, and Gordon Fleming, approach QFT from a variety of standpoints. Part I offers two different interpretations of the value of studying the foundations of QFT as an area of separate metaphysical research. Parts II and III consider the metaphysical and methodological implications of such issues as the problem of the status of virtual particles; the technique of renormalization; and the role of covariance principles. Part IV examines the mathematical foundations of QFT.
Quantum field theory (QFT) can be analyzed in terms of its mathematical structure, its conceptual scheme, or its basic ontology. The analysis can be done logically or historically. In this chapter, only the genesis of the conceptual foundations of QFT relevant to its basic ontology will be treated carefully; no detailed discussion of its mathematical structures or its epistemological underpinnings will be given. Some conceptual problems, such as those related to probability and measurement, will be discussed, but only because of their relevance to the basic ontology of QFT, rather than their intrinsic philosophical interest.
Abstract This is the first of a two‐part introduction to some interpretive questions that arise in connection with quantum field theories (QFTs). Some of these questions are continuous with those familiar from the discussion of ordinary non‐relativistic quantum mechanics (QM). For example, questions about locality can be rigorously posed and fruitfully pursued within the framework of QFT. A stark disanalogy between QFTs and ordinary QM – the former, but not the latter, typically admit infinitely many putatively physically inequivalent realizations – prompts relatively novel questions, questions about how to understand and adjudicate different strategies for equipping quantum theories with content. Part I sketches the fate of locality and related notions in QFT, then documents the non‐uniqueness unprecedented in ordinary QM but rampant in QFT. Part II presents foundations issues raised by non‐uniqueness.