# Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings

Guida, Riccardo and Konishi, Kenichi and Suzuki, Hiroshi (1996) Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings. Annals of physics, 249 (1). pp. 109-145. ISSN 1096-035X

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## Abstract

We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion - order dependent mappings (variational perturbation expansion) for the energy eigenvalues of anharmonic oscillator. For the single-well anharmonic oscillator the uniformity of convergence in $g\in[0,\infty]$ is proven. The convergence proof is extended also to complex values of $g$ lying on a wide domain of the Riemann surface of $E(g)$. Via the scaling relation \a la Symanzik, this proves the convergence of delta expansion for the double well in the strong coupling regime (where the standard perturbation series is non Borel summable), as well as for the complex `energy eigenvalues'' in certain metastable potentials. Sufficient conditions for the convergence of delta expansion are summarized in the form of three theorems, which should apply to a wide class of quantum mechanical and higher dimensional field theoretic systems.

Item Type: Article Imported from arXiv Area02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici Dipartimenti (from 2013) > DIPARTIMENTO DI FISICA dott.ssa Sandra Faita 11 Feb 2014 13:18 11 Feb 2014 13:18 http://eprints.adm.unipi.it/id/eprint/1664

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