论文标题
图形上的拉普拉斯和狄拉克操作员
Laplace and Dirac Operators on Graphs
论文作者
论文摘要
在统计力学和量子场理论的组合模型的背景下，研究了Laplace和Dirac Operators的离散版本。在本文中，我们在图上介绍了Laplace和Dirac运算符的几种变体，并研究了Schrödinger和Dirac方程的图理论版本。我们为方程解决方案提供了组合解释，并在晶格图以及图形Clifford代数上证明了Dirac运算符的胶合身份。
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.
