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Philosophy Compass

Ontologies for Quantum Field Theory

Luca Gasparinetti, Aaron Collavini

Published Nov 1, 2025• 0 citations
Publisher

Abstract

ABSTRACT This paper provides an overview of the ontological frameworks proposed for Quantum Field Theory (QFT). It begins by examining the conceptual challenges inherent in developing an ontology for QFT and outlines three potential ontological strategies. Subsequently, it surveys the principal ontological approaches discussed in the literature.

DOI
10.1111/phc3.70061

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ABSTRACT This paper provides an overview of the ontological frameworks proposed for Quantum Field Theory (QFT). It begins by examining the conceptual challenges inherent in developing an ontology for QFT and outlines three potential ontological strategies. Subsequently, it surveys the principal ontological approaches discussed in the literature.
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.
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.
The aim of this paper is to examine one of several candidates for the ontology of today’s most basic theory in physics, quantum field theory (QFT). I will begin by outlining some problems we encounter when we look at different conceptions for the basic entities to which QFT refers. The candidate ontology I wish to consider in this paper is process ontology. I shall characterize process ontology mainly in a negative manner as opposed to substance ontology. The central part will consist in a case study about how the interpretation of Feynman diagrams – the use of which is crucial in QFT – depends on whether we adhere to substance or process ontology. In conclusion I will evaluate my results and point towards some problems faced by process ontology as such.
Philosophical interpretations of theories generally presuppose that a theory can be presented as a consistent mathematical formulation that is interpreted through models. Algebraic quantum field theory (AQFT) can fit this interpretative model. However, standard Lagrangian quantum field theory (LQFT), as well as quantum electrodynamics and nuclear physics, resists recasting along such formal lines. The difference has a distinct bearing on ontological issues. AQFT does not treat particle interactions or the standard model. This paper develops a framework and methodology for interpreting such informal theories as LQFT and the standard model. We begin by summarizing two minimal epistemological interpretation of non-relativistic quantum mechanics (NRQM): Bohrian semantics, which focuses on communicables; and quantum information theory, which focuses on the algebra of local observables. Schwinger's development of quantum field theory supplies a unique path from NRQM to QFT, where each step is conceptually anchored in local measurements. LQFT and the standard model rely on postulates that go beyond the limits set by AQFT and Schwinger's anabatic methodology. The particle ontology of the standard model is clarified by regarding the standard model as an informal modular theory with a limited range of validity.
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.
There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.