论文标题
2、12、117、1959、45171、1170086，...：QCD手性拉格朗日的希尔伯特系列
2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian
论文作者
论文摘要
我们将希尔伯特系列技术应用于中间QCD手性拉格朗日的运营商的枚举。现有的Hilbert系列技术用于非线性实现，以纳入外部磁场。通过折叠$ \ frak {su}（n）$ dynkin图来解决电荷结合的动作，我们在附录中详细介绍，该附录可以单独读取，因为它具有潜在的更广泛的应用程序。新的结果包括以$ p^8 $命中出现在手性Lagrangian中的异常运算符，以及$ cp $ -even，$ cp $ -odd，$ c $ -odd和$ p $ -ODD项的枚举，从$ p^6 $开始。该方法可扩展到非常高的订单，我们提出结果为$ p^{16} $。 （标题序列是中介QCD手性Lagrangian中带有三种夸克的独立$ c $ -even $ p $ - p $ - even operators $ p^2 $，$ p^4 $，$ p^6 $，...）
We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $\frak{su}(n)$ Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order $p^8$, as well as enumeration of $CP$-even, $CP$-odd, $C$-odd, and $P$-odd terms beginning from order $p^6$. The method is extendable to very high orders, and we present results up to order $p^{16}$. (The title sequence is the number of independent $C$-even $P$-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions $p^2$, $p^4$, $p^6$, ...)
