A Groupoid Approach to the Riemann Integral (and Path Integral Quantization of the Poisson Sigma Model)
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911772418506752 |
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| author | Lackman, Joshua |
| author_facet | Lackman, Joshua |
| contents | We use groupoids and the van Est map to define Riemann sums on compact manifolds (with boundary), in a coordinate-free way. These Riemann sums converge to the usual integral after taking a limit over all triangulations of the manifold. We show that the van Est map determines the n-jet of antisymmetric n-cochains. We discuss using this Riemann sum construction to put the Poisson sigma model on a lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05640 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Groupoid Approach to the Riemann Integral (and Path Integral Quantization of the Poisson Sigma Model) Lackman, Joshua Differential Geometry High Energy Physics - Lattice Category Theory Symplectic Geometry We use groupoids and the van Est map to define Riemann sums on compact manifolds (with boundary), in a coordinate-free way. These Riemann sums converge to the usual integral after taking a limit over all triangulations of the manifold. We show that the van Est map determines the n-jet of antisymmetric n-cochains. We discuss using this Riemann sum construction to put the Poisson sigma model on a lattice. |
| title | A Groupoid Approach to the Riemann Integral (and Path Integral Quantization of the Poisson Sigma Model) |
| topic | Differential Geometry High Energy Physics - Lattice Category Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2309.05640 |