Laplace and Dirac Operators on Graphs
Mathematical Physics
2022-03-08 v1 Combinatorics
math.MP
Quantum Physics
Abstract
Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we introduce several variations of the Laplace and Dirac operators on graphs, and we investigate graph-theoretic versions of the Schr\"odinger and Dirac equation. We provide a combinatorial interpretation for solutions of the equations and we prove gluing identities for the Dirac operator on lattice graphs, as well as for graph Clifford algebras.
Keywords
Cite
@article{arxiv.2203.02782,
title = {Laplace and Dirac Operators on Graphs},
author = {Beata Casiday and Ivan Contreras and Thomas Meyer and Sabrina Mi and Ethan Spingarn},
journal= {arXiv preprint arXiv:2203.02782},
year = {2022}
}
Comments
36 pages, 25 figures