Da Costa, Lombardi and Lastiri (2013) have proposed an ontology of properties for non-relativistic quantum mechanics within the structure of the modal-Hamiltonian interpretation of the theory. Recently, this proposal has been developed in order to discuss the nature of entanglement and indistinguishability in such an ontology (Fortin and Lombardi 2022) and to explain how particles emerge from an ontology of properties (Lombardi and Dieks 2016). Oldofredi (2021) has also proposed an ontology of properties for Relational Quantum Mechanics. The aim of my paper is then to discuss an ontology of properties in the context of Quantum Field Theory (QFT). Wayne (2008) and Kuhlmann (2010) have already tried to define an ontology of properties for QFT in terms of tropes. However, I will try to follow a different approach. On the one hand, I will give a more general framework, which does not necessarily entail an ontology of tropes. I will in fact follow the path originally suggested by Da Costa, Lombardi and Lastiri, which is more general and formal. I will also briefly discuss how such an approach can be represented in an algebraic formalism. On the other hand, I will show how such an ontology of properties provides a good interpretation and representation of the measurement models that we can define in the context of QFT (by following the recent discussion of the measurement problem in QFT given by Grimmer 2022), and then of the experimental results.
The aim of this paper is to discuss a possible ontology of properties for quantum theories (QTs). The idea was originally formulated by Da Costa, Lombardi and Lastiri (2013) and has been quite ignored until recent years, when the original proposal has been developed and eventually generalized in order to cover other aspects of QTs, which were not properly analyzed in the original paper (see, for example, Holik, Jorge, Krause and Lombardi 2021 and Fortin and Lombardi 2022). Moreover, several scholars have recently considered different proposals of bundle theories as possible interpretations of QTs. In particular, Oldofredi (2021) has proposed a mereological bundle-theoretic interpretation of Rovelli’s Relational Quantum Mechanics (see Rovelli 1996 for the original formulation of Relational Quantum Mechanics). I do not want to enter in that debate in this paper, but I consider such a proposal as a good example of how an ontology of properties for QTs is still…
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