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• W4313251106 abstract "AbstractDiscrete versions of the Laplace and Dirac operators have 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 Schrödinger and Dirac equations. 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: Graph LaplacianDirac operatorSchrödinger's equationDirac's equationDimer modelClifford algebragraph gluing2020 Mathematics Subject Classifications: 05C1005C5005C3005C9081Q0581Q3515A67 AcknowledgmentsI.C. thanks Pavel Mnev for useful discussions during the early stages of this project. We also thank the anonymous referee for useful comments and suggestions.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research project started during the 2021 SUMRY Program at Yale University, which was supported by NSF [grant number DMS-2050398]." @default.
• W4313251106 created "2023-01-06" @default.
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• W4313251106 date "2022-12-26" @default.
• W4313251106 modified "2023-09-27" @default.
• W4313251106 title "Laplace and Dirac operators on graphs" @default.
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• W4313251106 doi "https://doi.org/10.1080/03081087.2022.2158297" @default.
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