A Trope Bundle Interpretation of Algebraic Quantum Field Theory

MCMP – Philosophy of Physics

Colloquium Mathematical Philosophy, Meinard Kuhlmann (Mainz) gives a talk at the MCMP Colloquium (10 December, 2014) titled "A Trope Bundle Interpretation of Algebraic Quantum Field Theory". Abstract: Algebraic quantum field theory (AQFT) is a conceptually lucid reformulation of the conventional theory of quantum fields. I consider AQFT to be the appropriate starting point for ontological considerations about QFT because, like the philosophical discipline of ontology, AQFT strives for a clear, justified and parsimonious separation of basic and derived classes of entities. I argue that the one-category theory of particularized properties or 'tropes', which analyses all other entities in terms of the basic category of tropes, yields the most appropriate ontological reading of AQFT. Among other things I will show that trope ontology and AQFT have essential structural similarities. I argue in particular that the trope-ontological conception of objects as bundles of tropes is related to the pivotal net structure of observable algebras in AQFT. Eventually, I show that the identification of trope-like entities in AQFT is best achieved via the notion of representations in the algebraic theory of superselection sectors, where the notion of inequivalent irreducible representations allows for a neat distinction of essential and non-essential properties/tropes.