具有自量子电荷的Maxwell场的奇异源
Singular Sources of Maxwell Fields with Self-Quantized Electric Charge
摘要：
考虑了真空中齐次麦克斯韦方程组的单值和多值解，其中“源”由场强的（点或弦状）奇异性形成，并且一般不可约为任何δ函数的分布。麦克斯韦方程组本身被视为一个主要的“超势”场的结果（例如，可积性条件），该场受到某些非线性和超定约束（特别是与扭量结构有关）。其结果是，我们得到（在显式或隐式代数形式）的麦克斯韦场的一个杰出的类，与奇异源必然携带一个“自量子化”的电荷整数倍的最小“基本”的。类粒子奇异体服从齐次麦克斯韦方程组的动力学方程，并经历不同类型的嬗变--分叉。所提出的方案源于作者开发的“代数动力学”方法，并在最后一节中进行了审查。附带地，建立了麦克斯韦方程组、复自对偶条件和Weyl "中微子“方程的解之间的基本等价关系，并简要地讨论了磁引力问题。
英文摘要：
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions' distribution. Maxwell equations themselves are treated as consequences (say, integrability conditions) of a primary ``superpotential'' field subject to some nonlinear and over-determined constraints (related, in particular, to twistor structures). As the result, we obtain (in explicit or implicit algebraic form) a distinguished class of Maxwell fields, with singular sources necessarily carrying a ``self-quantized'' electric charge integer multiple to a minimal ``elementary'' one. Particle-like singular objects are subject to the dynamics consistent with homogeneous Maxwell equations and undergo transmutations -- bifurcations of different types. The presented scheme originates from the ``algebrodynamical'' approach developed by the author and reviewed in the last section. Incidentally, fundamental equivalence relations between the solutions of Maxwell equations, complex self-dual conditions and of Weyl ``neutrino'' equations are established, and the problem of magnetic monopole is briefly discussed.
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