# Power series representations for complex bosonic effective actions. III. Substitution and fixed point equations

@article{Baaban2016PowerSR, title={Power series representations for complex bosonic effective actions. III. Substitution and fixed point equations}, author={Tadeusz Bałaban and Joel J. Feldman and Horst Knorrer and Eug{\`e}ne Trubowitz}, journal={Annales de l’Institut Henri Poincar{\'e} D}, year={2016} }

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…

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