复四程函方程的通解与“代数动力学”场论
General Solution of the Complex 4-Eikonal Equation and the "Algebrodynamical" Field Theory
摘要：
本文明确地证明了四维复化程函方程（CEE）的扭量和ambitwistor结构的存在性，并给出了由两类不同的解组成的通解。对于这两种情形，每一个解都可以通过一个生成扭量函数以纯代数的方式得到，其过程类似于无剪切零同余的克尔定理。程函或其梯度的有界奇点定义了一些具有非平凡特征和动力学的粒子状物体。本文给出了一个新的具有环状奇点的CEE静态解的例子，并简要讨论了与CEE密切相关的代数场论-代数动力学的一般原理。
英文摘要：
We explicitly demonstrate the existence of twistor and ambitwistor structure for the 4-dimensional complexified eikonal equation (CEE) and present its general solution consisting of two different classes. For both, every solution can be obtained from a generating twistor function in a purely algebraic way, via the procedure similar to that used in the Kerr theorem for shear-free null congruences. Bounded singularities of eikonal or of its gradient define some particle-like objects with nontrivial characteristics and dynamics. Example of a new static solution to CEE with a ring-like singularity is presented, and general principles of algebraic field theory - algebrodynamics - closely related to CEE are briefly discussed.
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