How to be a Relativistic Spacetime State Realist
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According to spacetime state realism (SSR), the fundamental ontology of a quantum mechanical world consists of a state-valued field evolving in 4-dimensional spacetime. One chief advantage it claims over rival wavefunction realist views is its natural compatibility with relativistic quantum field theory (QFT). I argue that the original density operator formulation of SSR cannot be extended to QFTs where the local observables form type III von Neumann algebras. Instead, I propose a new formulation of SSR in terms of a presheaf of local statespaces dual to the net of local observables studied by algebraic QFT.