极矩阵坐标中的拉普拉斯算子与高维径向费米子化
Laplacians in polar matrix coordinates and radial fermionization in higher dimensions
摘要：
我们考虑两个空间指数厄米矩阵的量子力学哈密顿量。通过引入矩阵值极坐标，得到了作用于不变态的拉普拉斯算子的形式。对于只依赖于径向矩阵特征值的势，我们建立了径向不变扇区等价于一个无相互作用的2+1维费米子系统，并得到了它的密度描述.对于较大数量的矩阵，一个排斥的径向本征值间的潜力的存在被确定。
英文摘要：
We consider the quantum mechanical hamiltonian of two, space indexed, hermitean matrices. By introducing matrix valued polar coordinates, we obtain the form of the laplacian acting on invariant states. For potentials depending only on the eigenvalues of the radial matrix, we establish that the radially invariant sector is equivalent to a system of non interacting 2+1 dimensional fermions, and obtain its density description. For a larger number of matrices, the presence of a repulsive radial inter-eigenvalue potential is identified.
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