标题： 规范化的Nambu-Jona-Lasinio模型的规范化的研究 显示英文标题

标题： Renormalization in the Gauged Nambu--Jona-Lasinio Model

摘要： 基于 Cornwall-Jackiw-Tomboulis 有效势，我们广泛研究了在阶梯近似下具有固定规范耦合的规范化的 Nambu-Jona-Lasinio 模型的非微扰重整化。尽管纯 Nambu-Jona-Lasinio 模型是不可重整化的，但规范相互作用的存在使得该理论能够在阶梯近似中的临界线上被重整化为一个相互作用的连续理论。不需要额外的高维算符（“反项”）来使该理论可重整化。借助有效势方法，重整化（“对称重整化”）以相独立的方式同时适用于手征对称的对称和自发破缺相。我们显式地得到了具有非平凡紫外不动点线的$\beta$函数，既包括重整化耦合也包括裸耦合。在两种相中，异常维度都非常大（$ \ge 1$），并且在不动点线处没有间断。明确构造了算符乘积展开，由于单位算符的 Wilson 系数中出现了非平凡的额外幂次行为，这与大的异常维度一致。对称重整化在临界规范耦合处失效，通过广义重整化方案（“$\tM$-依赖的重整化”）得以解决。还强调了它与少于四维空间中可重整的四费米子理论在$1/N$展开下的形式相似性。 显示英文摘要

摘要： Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in the ladder approximation with standing gauge coupling. Although the pure Nambu-Jona-Lasinio model is not renormalizable, presence of the gauge interaction makes it possible that the theory is renormalized as an interacting continuum theory at the critical line in the ladder approximation. Extra higher dimensional operators (``counter terms'') are not needed for the theory to be renormalized. By virtue of the effective potential approach, the renormalization (``symmetric renormalization'') is performed in a phase-independent manner both for the symmetric and the spontaneously broken phases of the chiral symmetry. We explicitly obtain $\beta$ function having a nontrivial ultraviolet fixed line for the renormalized coupling as well as the bare one. In both phases the anomalous dimension is very large ($ \ge 1$) without discontinuity across the fixed line. Operator product expansion is explicitly constructed, which is consistent with the large anomalous dimension owing to the appearance of the nontrivial extra power behavior in the Wilson coefficient for the unit operator. The symmetric renormalization breaks down at the critical gauge coupling, which is cured by the generalized renormalization scheme (``$\tM$-dependent renormalization''). Also emphasized is the formal resemblance to the four-fermion theory in less than four dimensions which is renormalizable in $1/N$ expansion.