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Divergence of perturbation theory: Steps towards a convergent series

Sergio A. Pernice

Gerardo Oleaga

  • Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627

  • Departamento de Matematica Aplicada, Facultad de Matematicas, Universidad Complutense, 28040 Madrid, Spain

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Phys. Rev. D 57, 1144 – Published 15 January, 1998

DOI: https://doi.org/10.1103/PhysRevD.57.1144

Abstract

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of Lebesgue’s dominated convergence theorem 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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Phys. Rev. D 57, 1144– Published 15 January, 1998
  • Received 14 August 1996

© 1998 American Physical Society

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