论文标题
$ \ mathfrak {su}（2）$ spin $ s $表示通过$ \ mathbb {c} p^{2S} $ sigma模型
The $\mathfrak{su}(2)$ spin $s$ representations via $\mathbb{C}P^{2s}$ sigma models
论文作者
论文摘要
我们建立并分析了描述旋转$ S $的任意组件的矩阵之间的新关系，其中$ 2S \ in \ mathbb {z}^+$与$ \ Mathbb {c} p^{2s} $二维Eucmenitional Euclidean Sigma模型。旋转矩阵是由Sigma模型的等级-1 Hermitian投影仪构建的，或者是由圆锥体的抗炎性函数在$ \ Mathfrak {su}（2S+1）$代数中构建的。对于可以表示为广义Pauli矩阵的线性组合的自旋矩阵，我们发现其系数满足的动力学方程。该方程被证明与二维Heisenberg模型的固定方程相同。我们表明，通过任何与坐标无关的统一线性变换，与普遍的Pauli的矩阵相一致的矩阵也是如此。这些属性为自旋新解释以及从统计力学到量子计算所描述的情况的新方法开辟了可能性。
We establish and analyze a new relationship between the matrices describing an arbitrary component of a spin $s$, where $2s\in \mathbb{Z}^+$, and the matrices of $\mathbb{C}P^{2s}$ two-dimensional Euclidean sigma models. The spin matrices are constructed from the rank-1 Hermitian projectors of the sigma models or from the antihermitian immersion functions of their soliton surfaces in the $\mathfrak{su}(2s+1)$ algebra. For the spin matrices which can be represented as a linear combination of the generalized Pauli matrices, we find the dynamics equation satisfied by its coefficients. The equation proves to be identical to the stationary equation of a two-dimensional Heisenberg model. We show that the same holds for the matrices congruent to the generalized Pauli ones by any coordinate-independent unitary linear transformation. These properties open the possibility for new interpretations of the spins and also for application of the methods known from the theory of sigma models to the situations described by the Heisenberg model, from statistical mechanics to quantum computing.
