# Towards synthetic Euclidean quantum field theory

### APA

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

### MLA

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

### BibTex

@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

## 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.