Abstract The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra Cl (3, 1) these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental physics and the Clifford geometry of Spacetime.

C. J. Robson

Advances in Applied Clifford Algebras

ADVANCES IN APPLIED CLIFFORD ALGEBRAS (AACA) 在 CLIFFORD 代数及其在数学、物理、工程和相关领域的其他分支中的应用领域发表高质量的同行评审研究论文以及说明性和调查性文章。该杂志确保快速出版，分为六个部分：分析、微分几何和狄拉克算子、数学结构、理论和数学物理、应用和书评。

The journal "Advances in Applied Clifford Algebras" focuses on Clifford algebras and their applications in mathematics, physics, engineering, and related fields. It publishes high-quality peer-reviewed research papers, as well as expository and survey articles, ensuring rapid publication. The journal is divided into six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.

《Advances in Applied Clifford Algebras》期刊专注于克利福德代数及其在数学、物理、工程及相关领域的应用。该期刊发表高质量的同行评审研究论文，以及说明性和调查性文章，确保快速出版。期刊内容分为六个部分：分析、微分几何与狄拉克算子、数学结构、理论与数学物理、应用以及书评。

Category	Quartile
数学	2
数学, 应用数学	2
数学, 物理数学物理	2

Self-Dual Maxwell Fields from Clifford Analysis

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	3