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Annales de l’Institut Henri Poincaré D


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Volume 6, Issue 1, 2019, pp. 43–71
DOI: 10.4171/AIHPD/64

Published online: 2018-07-25

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

Tadeusz Balaban[1], Joel Feldman[2], Horst Knörrer[3] and Eugene Trubowitz[4]

(1) Rutgers, The State University of New Jersey, Piscataway, USA
(2) University of British Columbia, Vancouver, Canada
(3) ETH Zürich, Switzerland
(4) ETH Zürich, Switzerland

In [3, 4, 5] we 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.

Keywords: Polymer-like expansion, renormalization group

Balaban Tadeusz, Feldman Joel, Knörrer Horst, Trubowitz Eugene: Power series representations for complex bosonic effective actions. III. Substitution and fixed point equations. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), 43-71. doi: 10.4171/AIHPD/64