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Towards synthetic Euclidean quantum field theory



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Recording Details

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PIRSA Number: 
19040076

Abstract

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.