III. Philosophical Foundations of The Quantum Theory

NORMAN R. CAMPBELL

Haipeng Peng

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.

Henry Krips

Tian Yu Cao

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.

Brigitte Falkenburg, Harvey R. Brown, Rom Harré

Rom Harre & Harvey Brown both of the University of Oxford: Introduction I. QUANTUM FIELD THEORY AS AN OBJECT OF PHILOSOPHICAL STUDY: TWO VIEWS: Michael Redhead, University of Cambridge: A philosopher looks at quantum field theory James T. Cushing, University of Notre Dame: Foundational problems in and methodological lessons from quantum field theory II. THE PROBLEMS OF VIRTUAL PARTICLES AND RENORMALIZATION: Robert Weingard, Rutgers University: Virtual particles and the interpretation of quantum field theory Rom Harre: Parsing the amplitudes Paul Teller, University of Illinois: Three problems of renormalization III. COVARIANCE PRINCIPLES IN QUANTUM FIELD THEORY: Gordon N. Fleming, Pennsylvania State University: Hyperplane-dependent quantized fields and Lorentz invariance Tian-yu Cao, Trinity College, Cambridge: Gauge theory and the geometrization of fundamental physics IV. MATHEMATICAL FOUNDATIONS OF QUANTUM FIELD THEORY: Ray F. Streater, King's College, London: Why should anyone want to axiomatize quantum field theory? Simon Saunders, Wolfson College, Oxford: The algebraic notation of quantum field theory.