四元数分析与代数动力学
Quaternionic Analysis and the Algebrodynamics
摘要：
我们提出了“代数动力学”的方法，以场粒子理论的基础上的非线性推广的柯西-黎曼条件的非交换代数的四元数类型。对于复杂的四元数，理论是洛伦兹不变的，自然带有一些规范和扭量结构。点和弦状奇点被认为是粒子状的形成;它们的电荷是“自量子化的”。提出了一种新的由原双四元数代数的结构所诱导的“带附加相位的因果Minkowski几何”.在此几何背景下，简要讨论了奇点的自洽代数动力学（“双锥系综”）。
英文摘要：
We present the ``algebrodynamical'' approach to field-particle theory based on a nonlinear generalization of the Cauchy-Riemann conditions to non-commutative algebras of quaternion-like type. For complex quaternions the theory is Lorentz invariant and naturally carries some gauge and twistor structures. Point- and string-like singularities are considered as particle-like formations; their electric charge is ``self-quantized''. A novel ``causal Minkowski geometry with additional phase'' is presented that is induced by the structure of primordial biquaternion algebra. On this geometrical background a self-consistent algebraic dynamics of singularities (``ensemble of dublicons'') is briefly discussed.
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