论文标题
$ su（2n_f）$ spin-flavor Group中的旋转和风味投影操作员
Spin and flavor projection operators in the $SU(2N_f)$ spin-flavor group
论文作者
论文摘要
特殊单一$ su（n）$组的二次Casimir操作员用于构建投影操作员，该投影运算符可以分解其在不可缩小空间的张量产品中包含的任何还原有限尺寸的表示空间。尽管该方法足够通用，但它专门针对$ su（2n_f）\ to su（2）\ otimes su（n_f）$ spin-flovavormemetry symmetry Group，它出现在QCD的Baryon sector中，在大$ $ n_c $限制中，在$ n_f $ and $ n_f $和$ n_c $的情况下，是$ n_f $ and $ n_c $的数量。该方法可导致旋转和风味投影操作员的构建，这些操作员可以在分析$ 1/n_c $ operator扩展中实施。投影操作员的使用使人们可以成功地投射给定运算符的所需组件，并减去不需要的组件。 $ SU（2）$和$ SU（3）$中的一些明确示例已详细介绍。
The quadratic Casimir operator of the special unitary $SU(N)$ group is used to construct projection operators, which can decompose any of its reducible finite-dimensional representation spaces contained in the tensor product of two and three adjoint spaces into irreducible components. Although the method is general enough, it is specialized to the $SU(2N_f) \to SU(2)\otimes SU(N_f)$ spin-flavor symmetry group, which emerges in the baryon sector of QCD in the large-$N_c$ limit, where $N_f$ and $N_c$ are the numbers of light quark flavors and color charges, respectively. The approach leads to the construction of spin and flavor projection operators that can be implemented in the analysis of the $1/N_c$ operator expansion. The use of projection operators allows one to successfully project out the desired components of a given operator and subtract off those that are not needed. Some explicit examples in $SU(2)$ and $SU(3)$ are detailed.
