关于规范变换的狄拉克不完全分析
On Dirac's incomplete analysis of gauge transformations
摘要：
讨论了狄拉克对规范对称性的研究方法。我们密切关注的步骤，导致他从他的猜想有关发电机的规范变换{ \it在一个给定的时间} -以对比的共同看法规范变换作为地图从解决方案的运动方程到其他解决方案-他的决定，人工修改的动力学，用扩展的哈密尔顿算子（包括所有第一类约束）代替总哈密尔顿算子（仅包括主要第一类约束）。我们详细表明，狄拉克的分析是不完整的，在完成它，我们证明了狄拉克猜想的履行-在“非病理”的情况下-并不意味着任何需要修改的动态。我们举几个简单但重要的例子。
英文摘要：
Dirac's approach to gauge symmetries is discussed. We follow closely the steps that led him from his conjecture concerning the generators of gauge transformations {\it at a given time} --to be contrasted with the common view of gauge transformations as maps from solutions of the equations of motion into other solutions-- to his decision to artificially modify the dynamics, substituting the extended Hamiltonian (including all first-class constraints) for the total Hamiltonian (including only the primary first-class constraints). We show in detail that Dirac's analysis was incomplete and, in completing it, we prove that the fulfilment of Dirac's conjecture --in the "non-pathological" cases-- does not imply any need to modify the dynamics. We give a couple of simple but significant examples.
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