标题： 复玻色子有效作用的幂级数表示。 III. 替换和固定点方程 显示英文标题

标题： Power Series Representations for Complex Bosonic Effective Actions. III. Substitution and Fixed Point Equations

摘要： 我们之前开发了一种类似聚合物的展开方法，该方法适用于功能积分中的（有效）作用量是被积分场的解析函数的情况。在这里，我们开发了方法，以帮助在使用最陡下降法分析功能积分时应用这种技术。我们开发了一个巴拿赫不动点定理的版本，可用于构造和控制临界场，作为外部场的解析函数，并且有替换公式来控制当用临界场和涨落场之和代替积分场时范数的变化。 显示英文摘要

摘要： We have previously developed a polymer-like expansion that applies when the (effective) action in a functional integral is an analytic function of the fields being integrated. Here, we develop methods to aid the application of this technique when the method of steepest descent is used to analyze the functional integral. We develop a version of the Banach fixed point theorem that can be used to construct and control the critical fields, as analytic functions of external fields, and substitution formulae to control the change in norms that occurs when one replaces the integration fields by the sum of the critical fields and the fluctuation fields.