The Physical Mathematics of Segal Topoi and Strings
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909576932098048 |
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| author | Gauthier, Renaud |
| author_facet | Gauthier, Renaud |
| contents | We introduce a notion of dynamics in the setting of Segal topos, by considering the Segal category of stacks $\mathcal{X} = \text{dAff}_{\mathcal{C}}^{\, \sim, τ}$ on a Segal category $\text{dAff}_{\mathcal{C}}=$ L(Comm($\mathcal{C})^{op})$ as our system, and by regarding objects of $\mathbb{R}\underline{\text{Hom}}(\mathcal{X}, \mathcal{X})$ as its states. We develop the notion of quantum state in this setting and construct local and global flows of such states. In this formalism, strings are given by equivalences between elements of commutative monoids of $\mathcal{C}$, a base symmetric monoidal model category. The connection with standard string theory is made, and with M-theory in particular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13786 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Physical Mathematics of Segal Topoi and Strings Gauthier, Renaud Category Theory Algebraic Geometry 18N60, 14D23, 18F20, 18A22, 81T30 We introduce a notion of dynamics in the setting of Segal topos, by considering the Segal category of stacks $\mathcal{X} = \text{dAff}_{\mathcal{C}}^{\, \sim, τ}$ on a Segal category $\text{dAff}_{\mathcal{C}}=$ L(Comm($\mathcal{C})^{op})$ as our system, and by regarding objects of $\mathbb{R}\underline{\text{Hom}}(\mathcal{X}, \mathcal{X})$ as its states. We develop the notion of quantum state in this setting and construct local and global flows of such states. In this formalism, strings are given by equivalences between elements of commutative monoids of $\mathcal{C}$, a base symmetric monoidal model category. The connection with standard string theory is made, and with M-theory in particular. |
| title | The Physical Mathematics of Segal Topoi and Strings |
| topic | Category Theory Algebraic Geometry 18N60, 14D23, 18F20, 18A22, 81T30 |
| url | https://arxiv.org/abs/2204.13786 |