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arXiv 2004.14406hep-thhep-phnucl-th
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关于规范场理论的正则表述和庞加莱变换

On the canonical formulation of gauge field theories and Poincare transformations

Daniel N. Blaschke, Francois Gieres

备注：
43 pages; Version accepted for publication in Nucl. Phys. B. Includes the interpretation of results on Hamiltonian symmetry generators as well as a concise and unified derivation of the gauge invariant currents associated to conformal invariance
发表信息：
Nucl. Phys. B 965 (2021) 115366
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摘要：

我们解决经典规范场理论的哈密顿公式，同时提出的结果，其中一些并不完全是新的，虽然他们似乎并不为人所知。我们特别提到这样一个事实，即正则能量动量矢量$(P^μ)$和规范不变能量动量矢量$(P_{\textrm{inv}} ^μ)$都不会通过泊松括号产生规范场的时空平移：在一般规范中，必须考虑所谓的运动学能量动量矢量，在特定规范中，（就像电动力学中的辐射规范），人们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助推，并与“核子自旋危机”直接相关，因为质子的自旋涉及胶子角动量矢量的贡献，因此需要适当处理后者。最后，我们对不同的量子化方法（基于经典哈密顿公式的正则量子化，Gupta-Blewald，路径积分，BRST，协变正则方法）之间的关系进行了一些评论。

英文摘要：

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 $(P^μ)$ nor the gauge invariant energy momentum vector $(P_{\textrm{inv}} ^μ)$ 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).

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