偶数维球面上Cremmer-Scherk组态解的运动方程
Equations of Motion Solved by the Cremmer-Scherk Configuration on Even-Dimensional Spheres
摘要：
量子电动力学的低能有效理论的运动方程包含无限多的相互作用项，这使得它们难以求解。自对偶性质为研究这类方程的解提供了方便。本文考虑偶数维球面上非阿贝尔规范场系统的运动方程。证明了满足某些广义自对偶方程的Cremmer-Scherk组态成为由2 m +1个量的C^1类任意函数所给出的系统类的经典解。例如，由多迹项组成的拉格朗日量就包括在这一类中。这一结果可能会产生几个新的和有趣的研究方向，包括分类的行动相对于Cremmer-Scherk配置的稳定性条件。
英文摘要：
Equations of motion of low-energy effective theories of quantum electrodynamics include infinitely many interaction terms, which make them difficult to solve. The self-duality property has facilitated research on the solutions to these equations. In this paper, equations of motion of systems of non-Abelian gauge fields on even-dimensional spheres are considered. It is demonstrated that the Cremmer-Scherk configuration, which satisfies certain generalized self-duality equations, becomes the classical solution for the class of systems that are given by arbitrary functions of class C^1 of 2m+1 quantities. For instance, Lagrangians consisting of multi-trace terms are included in this class. This result is likely to generate several new and interesting directions of research, including the classification of actions with respect to the stability condition against the Cremmer-Scherk configuration.
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