Most philosophical discussion of the particle concept that is afforded by quantum field theory has focused on free systems. This paper is devoted to a systematic investigation of whether the particle concept for free systems can be extended to interacting systems. The possible methods of accomplishing this are considered and all are found unsatisfactory. Therefore, an interacting system cannot be interpreted in terms of particles. As a consequence, quantum field theory does not support the inclusion of particles in our ontology. In contrast to much of the recent discussion on the particle concept derived from quantum field theory, this argument does not rely on the assumption that a particulate entity be localizable.
Although the philosophical literature on the foundations of quantum …eld theory recognizes the importance of Haag's theorem, it does not provide a clear discussion of the meaning of this theorem. The goal of this paper is to make up for this de…cit. In particular, it aims to set out the implications of Haag's theorem for scattering theory, the interaction picture, the use of non-Fock representations in describing interacting …elds, and the choice among the plethora of the unitarily inequivalent representations of the canonical commutation relations for free and interacting …elds.
Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT which are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. At one end of the spectrum of variants of QFT is the version which is found in introductory textbooks and employed by most working physicists; this is the variant of QFT which introduces renormalization procedures to facilitate the calculation of scattering matrix elements. At the other end of the spectrum are axiomatic presentations of QFT, which are rigorous but remote from practical applications. New arguments are offered for basing the interpretation of QFT on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case.
Following the experimental discovery of the Higgs boson, physicists explained the discovery to the public by appealing to analogies with condensed matter physics. The historical root of these analogies is the analogies to models of superconductivity that inspired the introduction of spontaneous symmetry breaking (SSB) into particle physics in the early 1960s. We offer a historical and philosophical analysis of the analogies between the Higgs model of the electroweak (EW) interaction and the Ginsburg-Landau (GL) and Bardeen-Cooper-Schrieffer (BCS) models of superconductivity, respectively. The conclusion of our analysis is that both sets of analogies are purely formal in virtue of the fact that they are accompanied by substantial physical disanalogies. In particular, the formal analogies do not map the temporal, causal, or modal structures of SSB in superconductivity to temporal, causal, or modal structures in the Higgs model. These substantial physical disanalogies mean that analogies to models of superconductivity cannot supply the basis for the physical interpretation of EW SSB; however, an appreciation of the contrast between the physical interpretations of SSB in superconductivity and the Higgs model does help to some foundational issues. Unlike SSB in superconductivity, SSB in the Higgs sector of the Standard Model (without the addition of new physics) is neither a temporal nor a causal process. We discuss the implications for the 'eating' metaphor for mass gain in the Higgs model. Furthermore, the distinction between the phenomenological GL model and the dynamical BCS model does not carry over to EW models, which clarifies the desiderata for so-called 'dynamical' models of EW SSB (e.g., minimal technicolor). Finally, the development of the Higgs model is an illuminating case study for philosophers of science because it illustrates how purely formal analogies can play a fruitful heuristic role in physics.
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