Towards synthetic Euclidean quantum field theory


Fritz, T. (2019). Towards synthetic Euclidean quantum field theory. Perimeter Institute. https://pirsa.org/19040076


Fritz, Tobias. Towards synthetic Euclidean quantum field theory. Perimeter Institute, Apr. 08, 2019, https://pirsa.org/19040076


          @misc{ pirsa_PIRSA:19040076,
            doi = {10.48660/19040076},
            url = {https://pirsa.org/19040076},
            author = {Fritz, Tobias},
            keywords = {Mathematical physics},
            language = {en},
            title = {Towards synthetic Euclidean quantum field theory},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {apr},
            note = {PIRSA:19040076 see, \url{https://pirsa.org}}

Tobias Fritz Universität Innsbruck


In a synthetic approach to geometry and physics, one attempts to formulate an axiomatic system in purely logical terms, abstracting away from irrelevant "implementation details". In this talk, I will explain how intuitionistic logic and topos theory provide a synthetic theory of space, and then consider a (naive version of) Euclidean QFTs in terms of a conjectural elegant synthetic reformulation: a Euclidean QFT is nothing but a probability space in intuitionistic logic, extended by suitable modalities formalizing compact regions of space. Time permitting, I will sketch how this approach is roughly dual to AQFT, and/or how to define vacua in terms of the DLR equations. I am also hoping for feedback on how naive this approach really is in the light of renormalization.