标题： 规范理论变分原理的新解释。 I. 循环坐标对ADM分解的替代方法 显示英文标题

标题： New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split

摘要： 我展示了在规范理论中，包括作为3+1几何动力学的广义相对论，如何存在对辅助变量处理的歧义。 辅助变量可以事先在变分前被当作乘子坐标，或者被当作循环坐标的速度。 后一种处理方式通过辅助变量值的物理无意义性，同样适用于变分的端点（或端空间超曲面），因此这些端点是自由的而非固定的。 [这也被称为具有自然边界条件的变分。] 进一步的动力学工作原理，如Routhian约简和Dirac过程，被证明对此新形式有对应的平行方法。 新方案的一个优点是相应的作用量更明显地具有关系性。 虽然电势通常被视为乘子坐标，而Arnowitt、Deser和Misner也将时间位移和空间位移视为类似，但本文的方案考虑了新的{\it 通量}、{\it 实例化}和{\it 网格}变量，它们对应的速度分别是之前使用的上述变量。 本文对规范理论的思考方式还允许有趣的推广，这些将在第二篇论文中提供。 显示英文摘要

摘要： I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. [This is also known as variation with natural boundary conditions.] Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose corresponding velocities are, respectively, the abovementioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations, which shall be provided in a second paper.