四面体方程及其变体的Clifford求解器
Clifford Solver for the Tetrahedron Equation and its Variants
AI总结：
该研究针对三维时空散射过程衍生的四面体方程及其变体，证明Clifford代数可求解其常系数与含谱参数版本，并提出借助四面体解规范求解更高维单形方程的方案，推动三维可积性研究。
摘要：
在三维时空中考虑无穷长直线散射过程的所有可能标记方式时，会出现不同形式的四面体方程。这有望导出三维可积性，类似于Yang-Baxter方程。在三种可能性中，我们研究了其中两种及其变体。我们证明Clifford代数可求解所有这些方程的常系数版本和含谱参数版本。我们还提出了一种利用四面体解规范求解更高维单形方程的方案。
英文摘要：
The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional spacetime. This is expected to lead to three dimensional integrability, analogous to the Yang-Baxter equation. Among the three possibilities, we consider two of them and their variants. We show that Clifford algebras solve both the constant and the spectral parameter dependent versions of all of them. We also present a scheme for canonically solving higher simplex equations using tetrahedron solutions.
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