Towards An Approach to Hilbert's Sixth Problem: A Brief Review

Yuri Ximenes Martins, Rodney Josué Biezuner
2020 Zenodo  
In 1900 David Hilbert published his famous list of 23 problems. The sixth of them-the axiomatization of Physics-remains partially unsolved. In this work we will give a gentle introduction and a brief review to one of the most recent and formal approaches to this problem, based on synthetic higher categorical languages. This approach, developed by Baez, Schreiber, Sati, Fiorenza, Freed, Lurie and many others, provides a formalization to the notion of classical field theory in terms of twisted
more » ... ferential cohomologies in cohesive (∞, 1)-topos. Furthermore, following the Atiyah-Witten functorial style of topological quantum field theories, it provides a nonperturbative quantization for classical field theories whose underlying cohomology satisfies orientability and duality conditions. We follow a pedagogical and almost non-technical style trying to minimize the mathematical prerequisites. No categorical background is required.
doi:10.5281/zenodo.4031161 fatcat:iw4rt5wesndelixelfmcwpwbiy