We address the Hamiltonian formulation of classical gauge field theories while putting forward results some of which are not entirely new, though they do not appear to be well known. We refer in particular to the fact that neither the canonical energy momentum vector $(P^{\mu })$ nor the gauge invariant energy momentum vector $(P_{\mathrm{\text{inv}}}^{\mu })$ do generate space-time translations of the gauge field by means of the Poisson brackets: In a general gauge, one has to consider the so-called kinematical energy momentum vector and, in a specific gauge (like the radiation gauge in electrodynamics), one has to consider the Dirac brackets rather than the Poisson brackets. Similar arguments apply to rotations and to Lorentz boosts and are of direct relevance to the “nucleon spin crisis” since the spin of the proton involves a contribution which is due to the angular momentum vector of gluons and thereby requires a proper treatment of the latter. We conclude with some comments on the relationships between the different approaches to quantization (canonical quantization based on the classical Hamiltonian formulation, Gupta-Bleuler, path integrals, BRST, covariant canonical approaches).

我们讨论经典规范场论的汉密尔顿表述，同时提出一些结果，尽管它们似乎并不为人们所熟知，但它们并不是全新的。我们特别提到这样一个事实，即既没有规范的能量动量矢量$（P^{\mu }）$也不是规范不变能量动量矢量$（P_{\mathrm{\text{v}}}^{\mu }）$确实可以通过泊松括号产生轨距场的时空平移：在一般轨距中，必须考虑所谓的运动能动量矢量，而在特定轨距中（例如电动力学中的辐射轨距），必须考虑狄拉克括号而不是泊松括号。类似的论点适用于旋转和洛伦兹增强，并且与“核子自旋危机”直接相关，因为质子的自旋涉及贡献，这归因于胶子的角动量矢量，因此需要对胶子的角动量矢量进行适当的处​​理。我们以一些不同的量化方法之间的关系作为结束语（基于经典汉密尔顿公式，古普塔-布鲁勒，路径积分，BRST，协变规范方法）。