Title: One-matrix differential reformulation of two-matrix models Show Chinese title

Title: 一矩阵微分重新表述两矩阵模型

Abstract: Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix models using a formula by Itzykson and Zuber that allows diagonalizing differential operators with respect to matrix elements of Hermitian matrices. We detail the equivalence between the expressions obtained by diagonalizing the partition function in differential or integral formulation, which is not manifest at first glance. For one-matrix models, this requires transforming certain derivatives to variables. In the case of two-matrix models, the same computation leads to a new determinant formulation of the partition function, and we discuss potential applications to new orthogonal polynomials methods. Show Chinese abstract

Abstract: 微分重表述常用于场论的显式计算。 我们借助一个由Itzykson和Zuber提出的公式，推导出一种双矩阵模型的一矩阵微分表述，该公式允许相对于厄米矩阵的矩阵元对微分算子进行对角化。 我们详细说明了通过微分或积分形式对角化划分函数所得表达式之间的等价性，这种等价性起初并不明显。 对于一矩阵模型，这需要将某些导数转换为变量。 在双矩阵模型的情况下，相同的计算导致了划分函数的一种新的行列式表述，我们讨论了其在新的正交多项式方法中的潜在应用。