An important, and highly non-trivial, problem is proving the renormalizability and unitarity of quantized non-Abelian gauge theories. Lee and Zinn-Justin have given the first proof of the renormalizability of non-Abelian gauge theories in the spontaneously broken phase. An essential ingredient in the proof has been the observation, by Slavnov and Taylor, of a non-linear, non-local symmetry of the quantized theory, a direct consequence of Faddeev and Popov’s quantization procedure. After the introduction of non-physical fermions to represent the Faddeev-Popov determinant, this symmetry has led to the Becchi-Rouet-Stora-Tyutin fermionic symmetry of the quantized action and, finally, to the resulting Zinn-Justin equation, which makes it possible to solve the renormalization and unitarity problems in their full generality. For an elementary introduction to the discussion of quantum non-Abelian gauge field theories in the spirit of the article, see, for example, L. D. Faddeev, “Faddeev-Popov ghosts,” Scholarpedia 4 (4), 7389 (2009); A. A. Slavnov, “Slavnov-Taylor identities,” Scholarpedia 3 (10), 7119 (2008); C. M. Becchi and C. Imbimbo, “Becchi-Rouet-Stora-Tyutin symmetry,” Scholarpedia 3 (10), 7135 (2008); J. Zinn-Justin, “Zinn-Justin equation,” Scholarpedia 4 (1), 7120 (2009).

中文翻译：

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从斯拉诺夫泰勒身份到量规理论的重新规范化

一个重要且高度重要的问题是证明量化的非阿贝尔规范理论的可重归一性和统一性。Lee和Zinn-Justin给出了自发破裂阶段非阿贝尔规范理论的可重整性的第一个证据。证明中的一个重要成分是Slavnov和Taylor对量化理论的非线性，非局部对称性的观察，这是Faddeev和Popov量化过程的直接结果。在引入非物理费米子代表Faddeev-Popov行列式之后，这种对称性导致了量化作用的Becchi-Rouet-Stora-Tyutin费米子对称性，最后导致了所得的Zinn-Justin方程，可以全面解决重归一化和统一性问题。有关本文精神的量子非阿贝尔规范场论讨论的基本介绍，请参见LD Faddeev，“ Faddeev-Popov鬼魂”，Scholarpedia 4（4），7389（2009）；AA Slavnov，“ Slavnov-Taylor identities”，Scholarpedia 3（10），7119（2008）；CM Becchi和C.Imbimbo，“ Becchi-Rouet-Stora-Tyutin对称性”，Scholarpedia 3（10），7135（2008）; J. Zinn-Justin，“ Zinn-Justin方程”，Scholarpedia 4（1），7120（2009）。