标题： 任意旋转不变随机矩阵系综与超对称性 显示英文标题

标题： Arbitrary Rotation Invariant Random Matrix Ensembles and Supersymmetry

摘要： 我们将随机矩阵理论中的超对称方法推广到任意旋转不变的系综。 我们的精确方法进一步扩展了之前的一项工作，在该项工作中我们为一类与范数相关的随机矩阵系综构建了超对称表示。 在这里，我们在非常一般的条件下推导出一个超对称公式。 识别出一个投影算子，该算子提供了从普通空间到超空间的概率密度映射。 此外，证明了在傅里叶超空间中建立理论具有显著优势。 给出了相关函数的一般且精确表达式。 我们还展示了在当前的上下文中如何避免使用双曲对称性，其中并未使用非线性σ模型。 我们构建了任意虚增量位置在格林函数中的相关函数的精确超对称积分表示。 显示英文摘要

摘要： We generalize the supersymmetry method in Random Matrix Theory to arbitrary rotation invariant ensembles. Our exact approach further extends a previous contribution in which we constructed a supersymmetric representation for the class of norm-dependent Random Matrix Ensembles. Here, we derive a supersymmetric formulation under very general circumstances. A projector is identified that provides the mapping of the probability density from ordinary to superspace. Furthermore, it is demonstrated that setting up the theory in Fourier superspace has considerable advantages. General and exact expressions for the correlation functions are given. We also show how the use of hyperbolic symmetry can be circumvented in the present context in which the non-linear sigma model is not used. We construct exact supersymmetric integral representations of the correlation functions for arbitrary positions of the imaginary increments in the Green functions.