Power series representations for complex bosonic effective actions. III: Substitution and fixed point equations. (English) Zbl 1432.82005
In the present paper, the authors continue their earlier investigations (for Part I and II, see [the authors, J. Math. Phys. 51, No. 5, 053305, 30 p. (2010; Zbl 1310.82005); J. Math. Phys. 51, No. 5, 053306, 20 p. (2010; Zbl 1310.82006)]), where it has been developed a polymer-like expansion that applies when the action in a functional integral is an analytic function of the fields being integrated. In this work, it is developed methods to aid the application of that technique when the method of steepest descent is used to analyze the functional integral. Besides, it is given 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.
Reviewer: Farruh Mukhamedov (Kuantan)
MSC:
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 82B28 | Renormalization group methods in equilibrium statistical mechanics |
| 30D10 | Representations of entire functions of one complex variable by series and integrals |
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