Quantum Field Theory as a Problem of Resummation (Short guide to using summability methods)

Details Quantum Field Theory as a Problem of Resummation (Short guide to using summability methods) Quantum Field Theory as a Problem of Resummation (Short guide to using summability methods)

1992-06-19

arxiv.org/abs/hep-th/9206074v1

Physics

High Energy Physics

High Energy Physics - Theory

Plain latex, 82 pp, 8 figures (ask author)) PhD Thesis, Prague, July 1991

Scientific paper

Thesis includes review on the large order behaviour of perturbation theory in quantum mechanical and field theory models; generalization of the Borel summability and strong asymptotic conditions to various (including horn-shaped) regions; discussion of analytic aspects of perturbation theory; examples which demonstrate differences between the Borel summability and generalized one; application to the Rayleigh-Schr\"{o}dinger perturbation theory and to the definition of the operator valued functions. The new summability methods converges in the whole Mittag-Leffeler star of an analytical function and as such is useful for localization of singularities in the complex plane. Their position can be calculated even analytically provided large order behaviour of the Taylor series is known. Method can be implemented numerically as well.

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