Title: Fundamental theorem on gauge fixing at the action level Show Chinese title

Title: 规范固定作用量层面的基本定理

Abstract: Regardless of the long history of gauge theories, it is not well recognized under which condition gauge fixing at the action level is legitimate. We address this issue from the Lagrangian point of view, and prove the following theorem on the relation between gauge fixing and Euler-Lagrange equations: In any gauge theory, if a gauge fixing is complete, i.e., the gauge functions are determined uniquely by the gauge conditions, the Euler-Lagrange equations derived from the gauge-fixed action are equivalent to those derived from the original action supplemented with the gauge conditions. Otherwise, it is not appropriate to impose the gauge conditions before deriving Euler-Lagrange equations as it may in general lead to inconsistent results. The criterion to check whether a gauge fixing is complete or not is further investigated. We also provide applications of the theorem to scalar-tensor theories and make comments on recent relevant papers on theories of modified gravity, in which there are confusions on gauge fixing and counting physical degrees of freedom. Show Chinese abstract

Abstract: 无论规范理论有着悠久的历史，但人们并不清楚在什么条件下在作用量层面上进行规范固定是合理的。 我们从拉格朗日观点来探讨这个问题，并证明了关于规范固定与欧拉-拉格莱方程之间关系的定理：在任何规范理论中，如果规范固定是完整的，即规范函数由规范条件唯一确定，那么从规范固定的作用量导出的欧拉-拉格莱方程与从原始作用量补充规范条件导出的方程是等价的。 否则，在推导欧拉-拉格莱方程之前施加规范条件是不合适的，因为这通常会导致不一致的结果。 进一步研究了检查规范固定是否完整的原则。 我们还将该定理应用于标量-张量理论，并对近期有关修改引力理论的相关论文进行了评论，这些论文中存在关于规范固定和物理自由度计数的混淆。