Constraints from conformal covariance on the mixing of operators of lowest twist
Constraints from conformal covariance on the mixing of operators of lowest twist
复制标题
共形协方差对最低扭曲算子混合的约束
DOI：
10.1016/0550-3213(82)90542-9
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发表时间：
1982
期刊：
影响因子：
--
通讯作者：
Theophil Ohrndorf
中科院分区：
文献类型：
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作者：
Theophil Ohrndorf
在无质量QCD中，将反常维矩阵对角化为α中的一阶算子变换为共形群的表示。用反常Ward恒等式证明了这一点。只有一个子群，即所谓的共线共形群SU(1,1) = SO(2,1)，作用于最小扭转算子的受限类。在夸克场中构造了双线性和三线性局部算子塔。它们被认为是作用于基本夸克场的导数中的多项式：双线性算子由雅可比多项式给出，三线性算子由阿佩尔多项式给出。利用异常维矩阵的显式证明了所构造的双线性共线共形算子实际上是特征向量。由于共形三线性算子基是退化的，所以三线性算子混合矩阵的特征向量不是单独由共形协方差决定的。然而，通过采用保角基，独立算子的数量大大减少。
In massless QCD the operators which diagonalize the anomalous dimension matrix to first order in αsform representations of the conformal group. This is proved by using anomalous Ward identities. Only a subgroup, the so-called collinear conformal group SU(1, 1) ≅ SO(2, 1), acts on the restricted class of operators of lowest twist. Towers of local operators bilinear and trilinear in the quark fields are constructed. They are considered as polynomials in the derivatives acting on the basic quark fields: bilinear operators are given by Jacobi polynomials, trilinear operators by Appell's polynomials.By using the explicit form of the anomalous dimension matrix we verify that the constructed bilinear collinear conformal operators are in fact eigenvectors. As the conformal trilinear operator basis is degenerate, the eigenvectors of the mixing matrix of trilinear operators are not determined by conformal covariance alone. However, by taking a conformal basis the number of independent operators is reduced considerably.