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

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.
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https://hal.archives-ouvertes.fr/hal-02909681
Contributor : Yuri Ximenes Martins <>
Submitted on : Monday, August 24, 2020 - 7:12:12 PM
Last modification on : Thursday, August 27, 2020 - 3:06:09 AM

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Yuri Ximenes Martins, Rodney Josué Biezuner. Towards An Approach to Hilbert's Sixth Problem: A Brief Review. 2020. ⟨hal-02909681v2⟩

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