arXiv 2505.024682025-05hep-thgr-qcmath-phmath.MPquant-ph

重新审视规范理论中约束的放松

Revisiting the relaxation of constraints in gauge theories

Centre for Theoretical Physics, the British University in Egypt（埃及不列颠大学理论物理中心）；Department of High Energy and Elementary Particle Physics, Saint Petersburg State University（圣彼得堡国立大学高能及基本粒子物理系）；Petersburg Nuclear Physics Institute of National Research Centre “Kurchatov Institute”（库尔恰托夫国家研究中心彼得堡核物理研究所）

Alexey Golovnev, Kirill Russkov

备注：: 9 pages; the final version; some comments and a few references added
发表信息：: Physica Scripta 101 (2026) 105002
DOI：: 10.1088/1402-4896/ae478b

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AI总结：

本文重新审视规范理论中约束的放松现象，探讨了路径积分方法中通过零动量变量固定规范时的约束放松机制，并与扩展哈密顿量的量子化方法进行类比。

摘要：

最近有一些工作声称规范理论的路径积分量子化本质上需要放松拉格朗日约束。正如文献中也指出的，这当然是错误的，因为完全存在尊重约束的规范场量子化，同时将经典理论以这种方式进行改变的想法在其他工作中也多次出现。另一方面，在路径积分方法中所做的工作是通过零动量变量来固定一种规范。我们希望表明，这种放松通常是当在拉格朗日理论的行动原理水平上固定此类规范时通常发生的现象。此外，还有一种有趣的类比可以引出。即，规范理论的一种量子化方法是构建一个扩展的哈密顿量，然后手动添加新的条件，使其成为二类系统。当在总哈密顿量的水平上做同样的事情时，即一个只有初级约束的二类系统时，约束的放松就会发生。

英文摘要：

Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist gauge field quantisations respecting the constraints, and at the same time the very idea of changing the classical theory in this way has many times appeared in other works. On the other hand, what was done in the path integral approach is fixing a gauge in terms of zero-momentum variables. We would like to show that this relaxation is what normally happens when one fixes such a gauge at the level of action principle in a Lagrangian theory. Moreover, there is an interesting analogy to be drawn. Namely, one of the ways to quantise a gauge theory is to build an extended Hamiltonian and then add new conditions by hand such as to make it a second class system. The constraints' relaxation occurs when one does the same at the level of the total Hamiltonian, i.e. a second class system with the primary constraints only.

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