The calculus of integration by parts, developed in Chapter 9 for finite volume theories; extends to the infinite volume measures dµ constructed in Chapter 11. These basic identities generate series which exhibit regularity and other detailed properties of the quantum field models. The integration by parts identities generate the perturbation expansion of Sections 8.4, 9.4 as well as the high and low temperature expansions studied in Part III and in the literature. These tools allow a detailed investigation of the local (ultraviolet) singularities of the models on the one hand and the large distance (infrared) decoupling on the other.
KeywordsInfinite Volume Wick Polynomial Cauchy Integral Theorem Wick Power Quantum Field Model
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