Improved convergence proof of the delta expansion and order dependent mappings

Journal Article · Mon Jul 01 04:00:00 EDT 1996 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1996.0066· OSTI ID:383711

Guida, R ^[1]; Konishi, K ^[1]; Suzuki, H ^[2]

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1. Dipartimento di Fisica, Universita di Genova, Via Dodecaneso, 33, Genoa, 16146 (Italy)
2. Department of Physics, Ibraki University, Mito, 310 (Japan)

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 {ital g}{element_of}[0,{infinity}] is proven. The convergence proof is extended also to complex values of {ital g} lying on a wide domain of the Riemann surface of {ital E}({ital g}). Via the scaling relation {grave 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 {open_quote}{open_quote}energy eigenvalues{close_quote}{close_quote} 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. Copyright {copyright} 1996 Academic Press, Inc.

• OSTI ID: 383711
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 249; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANHARMONIC OSCILLATORS
CONFORMAL MAPPING
CONVERGENCE
COUPLING CONSTANTS
CRITICAL EXPONENTS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM MECHANICS
SERIES EXPANSION
VARIATIONAL METHODS