Lattice electromagnetic theory from a topological viewpoint
Lattice electromagnetic theory from a topological viewpoint
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DOI：
10.1063/1.532767
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发表时间：
1999
影响因子：
1.3
通讯作者：
F. Teixeira;W. Chew
中科院分区：
文献类型：
--
作者：
F. Teixeira;W. Chew
用微分形式和拓扑概念的语言研究了晶格上的经典电磁理论。结果表明，微分形式及其离散对应物（协链）在理论的连续体和晶格版本之间提供了一个天然的桥梁，允许将场方程自然分解为拓扑场方程（即，同胚下的不变量）和度量场方程。在离散化过程中，各种潜在的不一致的来源被识别、区分和讨论。考虑了将晶格理论一致地推广到更一般的情况，如不规则晶格的基本原理。
The language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice. It is shown that differential forms and their discrete counterparts (cochains) provide a natural bridge between the continuum and the lattice versions of the theory, allowing for a natural factorization of the field equations into topological field equations (i.e., invariant under homeomorphisms) and metric field equations. The various potential sources of inconsistency in the discretization process are identified, distinguished, and discussed. A rationale for a consistent extension of the lattice theory to more general situations, such as to irregular lattices, is considered.