论文标题
晶格量表理论的Quasicharacters，重耦演算和特性
Quasicharacters, recoupling calculus and costratifications of lattice quantum gauge theory
论文作者
论文摘要
我们研究了紧凑型谎言组的副本副本上不变代表函数的代数代数函数。我们构建一个不变的代表函数的基础，称为Quasicharacters。 Quasicharacters的形式取决于还原方案的选择。我们确定了准腔的乘法定律，并根据恢复系数表达其结构常数。通过此链接，减少方案的选择可以从二元树方面获得解释。我们明确地表明，结构常数通过9J符号类型的原始元素分解为产品。对于SU（2），一切都归结为角动量理论的组合。在最后一部分中，我们表明上述演算使我们能够计算量子晶格仪理论中发生的双不可变化算子的矩阵元素。特别是，可以通过这种方式处理量子哈密顿量和轨道类型关系，从而减少了特定化的构建和光谱问题的研究，从而将线性代数的数值问题降低。我们阐明了g = su（2）的光谱问题，并提出了量规组su（2）和su（3）轨道类型关系矩阵元素的样本计算。开发的方法可能在研究几乎所有具有与某些对称性有关的多项式约束的量子模型的研究中很有用。
We study the algebra of invariant representative functions over the N-fold Cartesian product of copies of a compact Lie group G modulo the action of conjugation by the diagonal subgroup. We construct a basis of invariant representative functions referred to as quasicharacters. The form of the quasicharacters depends on the choice of a reduction scheme. We determine the multiplication law of quasicharacters and express their structure constants in terms of recoupling coefficients. Via this link, the choice of the reduction scheme acquires an interpretation in terms of binary trees. We show explicitly that the structure constants decompose into products over primitive elements of 9j symbol type. For SU(2), everything boils down to the combinatorics of angular momentum theory. In the final part, we show that the above calculus enables us to calculate the matrix elements of bi-invariant operators occuring in quantum lattice gauge theory. In particular, both the quantum Hamiltonian and the orbit type relations may be dealt with in this way, thus, reducing both the construction of the costratification and the study of the spectral problem to numerical problems in linear algebra. We spell out the spectral problem for G=SU(2) and we present sample calculations of matrix elements of orbit type relations for the gauge groups SU(2) and SU(3). The methods developed may be useful in the study of virtually all quantum models with polynomial constraints related to some symmetry.
