arXiv 1712.040732017-12-11hep-th

关于规范不变算子$A_{\min }^{2}$的规范固定不动点的可重正化类

On a renormalizable class of gauge fixings for the gauge invariant operator $A_{\min }^{2}$

M. A. L. Capri, D. M. van Egmond, G. Peruzzo, M. S. Guimaraes, O. Holanda, S. P. Sorella, R. C. Terin, H. C. Toledo

DOI：: 10.1016/j.aop.2018.01.009

摘要：

通过沿规范轨道最小化$\int d^4x A^2$得到的二维规范不变非定域算符$A_{\min }^{2}$，引入了一个非定域规范不变组态$A^h_μ$，利用它建立了一类用于研究约束理论非微扰红外效应的有质量Yang-Mills模型.一个完全本地设置为$A_{\min }^{2}$和$A^{h}_μ$可以实现，导致在一个本地和BRST不变的行动，共享相似的Stueckelberg形式主义。然而，与施图克尔伯格作用量的情况不同，$A_{\min }^{2}$的使用产生了一个所有阶数的可重整作用量，这一特征将通过一类协变的规范固定来说明，它和胡夫特的自发破缺规范理论的$R_ζ$规范一样，为施图克尔伯格场提供了一个质量。

英文摘要：

The dimension two gauge invariant non-local operator $A_{\min }^{2}$, obtained through the minimization of $\int d^4x A^2$ along the gauge orbit, allows to introduce a non-local gauge invariant configuration $A^h_μ$ which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both $A_{\min }^{2}$ and $A^{h}_μ$ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of $A_{\min }^{2}$ gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as 't Hooft's $R_ζ$-gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field.

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