Sheaf Topos Theory: A powerful setting for Lagrangian Field Theory

Fuente: arXiv
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Autor principal: Giotopoulos, Grigorios
Formato: Preprint
Publicado: 2025
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author Giotopoulos, Grigorios
author_facet Giotopoulos, Grigorios
contents We provide an introductory exposition to the sheaf topos theoretic description of classical field theory motivated by the rigorous description of both $\bf{(i)}$ the variational calculus of (infinite dimensional) field-theoretic spaces, and $\bf(ii)$ the non-triviality of classical fermionic field spaces. These considerations naturally lead to the definition of the sheaf topos of super smooth sets. We close by indicating natural generalizations necessary to include to the description of infinitesimal structure of field spaces and further the non-perturbative description of (higher) gauge fields.
format Preprint
id arxiv_https___arxiv_org_abs_2504_08095
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Sheaf Topos Theory: A powerful setting for Lagrangian Field Theory
Giotopoulos, Grigorios
Mathematical Physics
High Energy Physics - Theory
Category Theory
We provide an introductory exposition to the sheaf topos theoretic description of classical field theory motivated by the rigorous description of both $\bf{(i)}$ the variational calculus of (infinite dimensional) field-theoretic spaces, and $\bf(ii)$ the non-triviality of classical fermionic field spaces. These considerations naturally lead to the definition of the sheaf topos of super smooth sets. We close by indicating natural generalizations necessary to include to the description of infinitesimal structure of field spaces and further the non-perturbative description of (higher) gauge fields.
title Sheaf Topos Theory: A powerful setting for Lagrangian Field Theory
topic Mathematical Physics
High Energy Physics - Theory
Category Theory
url https://arxiv.org/abs/2504.08095