双矩阵模型的单矩阵微分重构
One-matrix differential reformulation of two-matrix models
摘要：
场论的微分变换常用于显式计算。我们推导了两个矩阵模型的一个矩阵微分公式，利用Itzykson和Zuber的一个公式可以对角化一个和两个矩阵模型，该公式允许对角化关于厄米矩阵的矩阵元素的微分算子.我们详细介绍了对角化的配分函数在微分或积分公式，这是不明显的乍一看得到的表达式之间的等价性。对于单矩阵模型，这需要将某些导数转换为变量。在两个矩阵模型的情况下，相同的计算导致一个新的行列式制定的配分函数，我们讨论了潜在的应用新的正交多项式方法。
英文摘要：
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.
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