论文标题
关于theta和6J符号的整数值变体
About integer-valued variants of the theta and 6j symbols
论文作者
论文摘要
这些笔记本质上包含了两个众所周知的数量的几个属性，即所谓的theta符号（或三角形符号），这是理性的，而6J符号通常是不合理的，就两个相关的整数值称为GON和TET而言。这些相关的整数价值化身的存在，与他们更受欢迎的合作伙伴共享大多数基本特性，尽管这是一个已知的事实，但经常被忽略。在经典和量子情况下，GON和TET的特性比相应的Theta和6J符号的属性更容易获得或制定。他们的评估也更简单（本文显示了许多明确的公式和可能加快某些计算机程序的评估程序）。这两个整数值的功能是不寻常的，因为它们的属性似乎并不经常在文献中进行讨论，但是它们的功能反映了许多地方讨论的相关实现功能的功能。但是，我们将讨论的某些属性似乎是新的，特别是函数GON与Hilbert矩阵之间的几种关系。
These notes contain essentially a rewriting of several properties of two well-known quantities, the so-called theta symbol (or triangular symbol), which is rational, and the 6j symbol, which is usually irrational, in terms of two related integer-valued functions called gon and tet. Existence of these related integer-valued avatars, sharing most essential properties with their more popular partners, although a known fact, is often overlooked. The properties of gon and tet are easier to obtain, or to formulate, than those of the corresponding theta and 6j symbols, both in the classical and quantum situations. Their evaluation is also simpler (the paper displays a number of explicit formulae and evaluation procedures that may speed up some computer programs). These two integer-valued functions are unusual, in that their properties do not appear to be often discussed in the literature, but their features reflect those of related real-valued functions discussed in many places. Some of the properties that we shall discuss seem however to be new, in particular several relations between the function gon and the inverse Hilbert matrices.
