标题： 杨-米尔斯方程的自然对称性 显示英文标题

标题： Natural Symmetries of the Yang-Mills Equations

摘要： 我们定义了杨-米尔斯方程的一种自然广义对称性，即杨-米尔斯场的无穷小变换，它以局域的方式由杨-米尔斯场强及其任意阶导数组成，且保持规范不变性和庞加莱不变性，同时将场方程的解映射为其他解。 在杨-米尔斯联络的射流丛上，我们引入了一种旋量坐标系，该坐标系适应于由杨-米尔斯方程定义的解子空间。 利用这一坐标系，自然对称性的完整分类得以直接完成。 我们发现，杨-米尔斯方程的所有自然对称性均源自方程所允许的规范变换。 显示英文摘要

摘要： We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength and its derivatives to any order, which maps solutions of the field equations to other solutions. On the jet bundle of Yang-Mills connections we introduce a spinorial coordinate system that is adapted to the solution subspace defined by the Yang-Mills equations. In terms of this coordinate system the complete classification of natural symmetries is carried out in a straightforward manner. We find that all natural symmetries of the Yang-Mills equations stem from the gauge transformations admitted by the equations.