Spin and flavor projection operators in the SU(2Nf) spin-flavor group
Spin and flavor projection operators in the
SU(2Nf)
spin-flavor group
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SU(2Nf) 自旋风味群中的自旋和风味投影算子
DOI：
10.1103/physrevd.102.036010
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发表时间：
2020
影响因子：
5
通讯作者：
F. D. J. Rosales
中科院分区：
文献类型：
--
作者：
V. M. Banda Guzmán;R. Flores;Johann Hernández;F. D. J. Rosales
利用特殊酉$SU(N)$群的二次卡西米尔算子构造投影算子，该投影算子可以将其包含在二伴空间张量积中的任意可约有限维表示空间分解为不可约分量。虽然该方法足够通用，但它专门针对QCD重子扇区在大-$N_c$极限下出现的$SU(2N_f) \到SU(2)\o倍SU(N_f)$自旋风味对称群，其中$N_f$和$N_c$分别为轻夸克风味数和色荷数。该方法导致了旋转和风味投影算子的构造，可以在$1/N_c$算子展开的分析中实现。投影运算符的使用允许人们成功地投影出给定运算符的所需分量，并减去那些不需要的分量。详细介绍了$SU(2)$和$SU(3)$中一些显式的例子。
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.