Fraser, James D.
(2026)
Enacting Rigour: Global-Rebuilding and Local-Repair in Quantum Field Theory.
[Preprint]
Abstract
Quantum field theory (QFT) has long been subject to rigour concerns. Attempts to reformulate the theory in a more rigorous form have not converged on a single formalism, however, but have instead produced a plurality of distinct approaches. This chapter treats these reformulation programmes as a case study for investigating the methodological role of rigour in science. Tracing the development of axiomatic QFT and causal perturbation theory, I argue that these programmes instantiate distinct rigourisation strategies: a global-rebuilding strategy, which seeks to reconstruct the target theory starting from a new mathematical foundation, and a local-repair strategy, which aims to resolve specific points of unclarity within the existing formalism. The philosophical upshot is that we need to conceive of rigour as an ideal that is enacted differently on different methodological pathways. I briefly touch on how this framework might be extended to other areas of mathematics, science, and philosophy where rigour concerns loom large.
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