论文标题
来自多项式线性化的分数dirac方程：解决方案和困难
Fractional Dirac Equations from Polynomial Linearization: Solutions and Difficulties
论文作者
论文摘要
二次形式的线性化产生了Clifford代数结构，如Dirac对D'Alembert操作员的分解所示。类似的结构被称为广义的克利福德代数源于该程序对高阶形式的延续。该技术与满足半组属性的分数衍生物的存在相结合，可用于进一步考虑D'Alembert操作员，从而产生与Dirac方程相似形式的分数部分差分矩阵方程。我们检查了这些方程式，它们的解决方案，并指出了试图使它们有理有意识时的困难。
The linearization of a quadratic form gives rise to a Clifford algebra structure, as seen in Dirac's factorization of the d'Alembert operator. A similar structure known as a generalized Clifford algebra arises from the continuation of this procedure to higher order forms. This technique combined with the existence of a fractional derivative satisfying the semi-group property can be used to factor the d'Alembert operator further, producing a fractional partial differential matrix equation that has a similar form to Dirac's equation. We examine these equations, their solutions, and point out difficulties when attempting to make physical sense of them.
