八元数中离散斯托克斯公式的外尔微积分视角
Weyl calculus perspective on the discrete Stokes' formula in octonions
AI总结：
针对离散八元数分析中外尔微积分方法的研究空白，本文基于外尔微积分提出八元数分析的离散化方法，以满足实际应用中直接研究离散结构的需求。
摘要：
八元数是8维超复数，构成实数域上最大的赋范可除代数。受理论物理应用的启发，连续八元数分析近年来已成为活跃的研究领域。考虑到可能的实际应用，直接研究离散结构而非近似连续对象更为有益。因此，在先前的论文中，我们提出了一些关于离散八元数分析的想法。众所周知，离散化连续设置有多种可能性，而在离散克利福德分析中常用的外尔微积分方法尚未应用于八元数研究。为此，本文通过提出基于外尔微积分的八元数分析离散化方法填补了这一空白。
英文摘要：
Octonions are 8-dimensional hypercomplex numbers which form the biggest normed division algebras over the real numbers. Motivated by applications in theoretical physics, continuous octonionic analysis has become an area of active research in recent year. Looking at possible practical applications, it is beneficial to work directly with discrete structures, rather than approximate continuous objects. Therefore, in previous papers, we have proposed some ideas towards the discrete octonionic analysis. It is well known, that there are several possibilities to discretise the continuous setting, and the Weyl calculus approach, which is typically used in the discrete Clifford analysis, to octonions has not been studied yet. Therefore, in this paper, we close this gap by presenting the discretisation of octonionic analysis based on the Weyl calculus.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
