A Groupoid Approach to the Riemann Integral (and Path Integral Quantization of the Poisson Sigma Model)
Differential Geometry
2024-02-08 v2 High Energy Physics - Lattice
Category Theory
Symplectic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2309.05640,
title = {A Groupoid Approach to the Riemann Integral (and Path Integral Quantization of the Poisson Sigma Model)},
author = {Joshua Lackman},
journal= {arXiv preprint arXiv:2309.05640},
year = {2024}
}