标题： O(n) 四次矩阵模型及其在计算交错结和链环中的应用 显示英文标题

标题： The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links

摘要： 本文在一个统一的框架下，利用应用于彩色链矩阵模型的量子场论方法，按照交错扭结的数量、外部腿的数量和连通分支的数量对其进行计数。 通过矩阵模型的重整化方案消除了与图拓扑等价相关的过量计数；导出了相应的“重整化方程”。 一些特殊情况被详细研究并精确求解。 显示英文摘要

摘要： The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding ``renormalization equations'' are derived. Some particular cases are studied in detail and solved exactly.