Higher Category Theory and Hilbert's Sixth Problem - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2021

Higher Category Theory and Hilbert's Sixth Problem

Abstract

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 differential 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.
Fichier principal
Vignette du fichier
axiomatization_physics.pdf (387.75 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02909681 , version 1 (30-07-2020)
hal-02909681 , version 2 (24-08-2020)
hal-02909681 , version 3 (30-12-2021)

Identifiers

  • HAL Id : hal-02909681 , version 3

Cite

Yuri Ximenes Martins, Rodney Josué Biezuner. Higher Category Theory and Hilbert's Sixth Problem. 2021. ⟨hal-02909681v3⟩

Collections

TDS-MACS
449 View
1103 Download

Share

Gmail Facebook X LinkedIn More