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Oleaga Apadula, Gerardo Enrique and Pernice, Sergio A. (1998) Divergence of perturbation theory: Steps towards a convergent series. Physical Review D, 57 (2). pp. 11441158. ISSN 15507998

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Official URL: http://prd.aps.org/pdf/PRD/v57/i2/p1144_1
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http://prd.aps.org/  Publisher 
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 deltaexpansion; Connected vacuum amplitude; Order dependent mappings; Quantumfield theory; Anharmonicoscillator; Variational calculation; Nonlinearsystems; Zero dimensions; Proof; Approximations 
Subjects:  Sciences > Mathematics > Differential equations 
ID Code:  17294 
Deposited On:  03 Dec 2012 10:38 
Last Modified:  12 Dec 2018 15:07 
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