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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
36/2022

Gauge theory on graphs

Shuhan Jiang

Abstract

In this paper, we provide the notions of connections, exterior covariant derivatives, and connection Laplacians on a graph. We prove a Weitzenböck formula in this setting. We also define a discrete Yang-Mills functional and study the solutions to its Euler-Lagrange equations.

Received:
Dec 2, 2022
Published:
Dec 2, 2022
MSC Codes:
05C10

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2022 Repository Open Access
Shu-Han Jiang

Gauge theory on graphs