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Divergence of perturbation theory: Steps towards a convergent series

Oleaga Apadula, Gerardo Enrique and Pernice, Sergio A. (1998) Divergence of perturbation theory: Steps towards a convergent series. Physical Review D , 57 (2). 1144-1158 . ISSN 1550-7998

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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 held 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.

Item Type:Article
Uncontrolled Keywords:Optimized delta-expansion; Connected vacuum amplitude; Order dependent mappings; Quantum-field theory; Anharmonic-oscillator; Variational calculation; Nonlinear-systems; Zero dimensions; Proof; Approximations
Subjects:Sciences > Mathematics > Differential equations
ID Code:17294
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