Varieties of Rigour: Charting the Landscape of Reformulation Programmes in 1950 Quantum Field Theory

          @misc{ scivideos_PIRSA:25100073,
            doi = {10.48660/25100073},
            url = {https://pirsa.org/25100073},
            author = {},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Varieties of Rigour: Charting the Landscape of Reformulation Programmes in 1950 Quantum Field Theory},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100073 see, \url{https://scivideos.org/pirsa/25100073}}
          }
          

Abstract

Historians and philosophers of quantum field theory (QFT) face a distinctive challenge: the existence of multiple, mathematically and conceptually divergent formulations of the theory. Discussions of this issue in the extant literature often contrast the mainstream perturbative formalism—empirically powerful but mathematically dubious—with axiomatic QFT—mathematically rigorous but largely detached from empirical predictions. This paper complicates this dichotomy by drawing attention to a parallel tradition, beginning in the 1950s, that sought to render perturbative QFT itself more rigorous. One way to think about this is that there is considerable diversity even within the “mathematical QFT” camp. In order to account for this, I suggest that the axiomatic QFT and causal perturbation theory traditions can be understood as adopting distinct ideals of mathematical rigour: a global and a local conception, respectively.