Laplace and Dirac Operators on Graphs

2022/03/05 by Beata Casiday, Iván Contreras, Casiday, Beata +7 · 2 citations
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2203.02782

openalex publication_date 2022/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrödinger 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.

Cited by

• Supersymmetry Breaking in Graph Quantum Mechanics
• FoGE: Fock Space inspired encoding for graph prompting

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