Improved convergence proof of the delta expansion and order dependent mappings

Riccardo Guida, Kenichi Konishi, Hiroshi Suzuki

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


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 quartic anharmonic oscillator. For the single-well oscillator the uniformity of convergence in g∈[0, ∞] 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 à 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 systems. Difficulties in extending the convergence proof to the cases of higher anharmonic oscillators are pointed out. Sufficient conditions for the convergence of delta expansion are summarized in the form of three general theorems, which should apply to a wide class of quantum mechanical and higher dimensional field theoretic systems.

Original languageEnglish
Pages (from-to)109-145
Number of pages37
JournalAnnals of Physics
Issue number1
Publication statusPublished - Jul 10 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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