构造拉格朗日函数的希尔伯特级数：扩展现象学家的工具箱
Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
摘要：
本说明介绍了希尔伯特级数技术，以更广泛的观众在建设组不变拉格朗日。这种技术提供了一种快速的方法来计算一个特定的质量维度的运营商的数量为一个给定的字段内容，是一个有用的交叉检查更知名的群论方法。此外，至少当限制到不含导数的不变量时，希尔伯特级数技术提供了一种鲁棒的方法来计算场景中的不变量，由于涉及大量的字段或高维群表示，传统方法难以处理。我们提出了几个实际的例子。
英文摘要：
This note presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content, and is a useful cross check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high dimensional group representations, are intractable by traditional methods. We work out several practical examples.
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