与电磁场相互作用的复杂空间局域场
Complex space-localized fields interacting with electromagnetic fields
摘要：
已知几类非线性场方程具有空间局部化的无奇性解，这些解描述了具有有限厄米范数的场。本文研究这类场与给定电磁势的相互作用，通过协变导数形式进入场的方程。主要结果是：如果在一些非常普遍和物理上有意义的假设下，空间局域场是非线性薛定谔方程或非线性狄拉克方程的解，那么空间局域场的运动作为一个整体，与在相同电磁势中运动的点电荷的运动本质上是相同的。使用另一种方法，类似的结果是持有一类非常广泛的非线性场方程。
英文摘要：
Several families of nonlinear field equations are known to possess space- localized singularity-free solutions which describe fields with finite Hermitian norms. This paper studies the interaction of such fields with given electromagnetic potentials entering the field's equations through the covariant derivative form. The main result is: the motion of a space-localized field, as a whole, is essentially identical to that of a point charge moving in the same electromagnetic potentials, if this field is a solution either to a nonlinear Schrodinger or to a nonlinear Dirac equation, under some very general and physically meaningful assumptions. Using an alternative method, similar result is shown to hold for a very wide class of nonlinear field equations.
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