规范理论变分原理的新解释。I.循环坐标替代ADM分割
New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
摘要：
我展示了如何在规范理论包括广义相对论中把辅助变量当作3 + 1几何动力学来处理，这是一个模棱两可的问题。辅助变量可以被预变分地处理为乘数坐标或对应于循环坐标的速度。后一种处理通过辅助变量值的物理无意义也适用于变分的端点（或末端空间超曲面），因此这些是自由的而不是固定的。[This也称为自然边界条件下的变分。进一步的原则，如Routhian减少和狄拉克程序的动力学工作有平行的对应物，这种新的形式主义。新方案的一个优点是，相应的行动是更明显的关系。虽然电势通常被视为一个乘数坐标和Arnowitt，Deser和Misner认为同样的推移和移位，本文的计划认为新的{ \it通量}，{ \it瞬间}和{ \it网格}变量，其相应的速度，分别是上述以前使用的变量。本文对规范理论的思考方式还承认有趣的推广，这将在第二篇论文中提供。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
