标题： 玻尔兹曼场论中的相互作用表示 显示英文标题

标题： Interaction Representation in Boltzmann Field Theory

摘要： 我们考虑玻尔兹曼场论中的相互作用表示。 它描述了矩阵模型中一类平面图的主场，即所谓的半平面图。 这种相互作用表示由阿卡德里、沃洛维奇和其中一位作者（I.A.）在之前的一篇论文中发现， 并且它具有一种非同寻常的性质，即人们处理的是相互作用拉格朗日的有理函数，而不是普通的指数函数。 在这里，我们更详细地研究了相互作用表示，并证明在自然假设下，该表示实际上是唯一的。 我们展示了相应的施温格-戴森方程导致了两个和四个点关联函数的封闭积分方程组。 对该模型进行了重整化，并得到了重整化群方程。 用一些离散自由度的模型例子进行了数值求解。 对于一个自由度的解与一个矩阵模型的平面近似进行了比较。 对于大量的耦合常数，它以良好的精度再现了平面近似。 显示英文摘要

摘要： We consider an interaction representation in the Boltzmann field theory. It describes the master field for a subclass of planar diagrams in matrix models, so called half-planar diagrams. This interaction representation was found in the previous paper by Accardi, Volovich and one of us (I.A.) and it has an unusual property that one deals with a rational function of the interaction Lagrangian instead of the ordinary exponential function. Here we study the interaction representation in more details and show that under natural assumptions this representation is in fact unique. We demonstrate that corresponding Schwinger-Dyson equations lead to a closed set of integral equations for two- and four-point correlation functions. Renormalization of the model is performed and renormalization group equations are obtained. Some model examples with discrete number of degrees of freedom are solved numerically. The solution for one degree of freedom is compared with the planar approximation for one matrix model. For large variety of coupling constant it reproduces the planar approximation with good accuracy.