On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

Details On the Divergence of Perturbation Theory. Steps Towards a Convergent Series On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

1996-09-17

arxiv.org/abs/hep-th/9609139v1

Phys.Rev. D57 (1998) 1144-1158

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, Latex, 4 figures

Scientific paper

10.1103/PhysRevD.57.1144

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.

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