论文标题
关于约束和自由程度在哈密顿形式主义中的作用
On the role of constraints and degrees of freedom in the Hamiltonian formalism
论文作者
论文摘要
不幸的是，堕落的拉格朗日系统的哈密顿力学通常是作为狄拉克的一种食谱，没有关于其工作原理的解释。然后，讨论所有主要约束是否对应于量学对称性的猜想，并且它一直涉及绝对错误的主张，例如陈述电动力学或重力只有两个物理成分，而另一些则具有虚假。必须非常小心，因为非动力或受约束并不意味着非物理。我对堕落的哈密顿系统进行了教学介绍，展示了非常简单的机械示例和有关其工作原理的一般论点。对于熟悉的现场理论模型，我解释了为什么那里的仪表自由在产生两倍的一流约束意义上是量规对称性的两倍，以及为什么主要的且只有主要的约束才能放入汉密尔顿总体中。
Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. Then it comes to discussing conjectures of whether all primary constraints correspond to gauge symmetries, and it goes all the way to absolutely wrong claims such as the statement that electrodynamics or gravity have only two physical components each, with others being spurious. One has to be very careful because non-dynamical, or constrained, does not mean unphysical. I give a pedagogical introduction to the degenerate Hamiltonian systems, showing both very simple mechanical examples and general arguments about how it works. For the familiar field theory models, I explain why the gauge freedom there "hits twice" in the sense of producing twice as many first-class constraints as gauge symmetries, and why primary, and only primary, constraints should be put into the total Hamiltonian.
