Borel summation of divergent series in field theory and Wynn's element of algorithm

Journal Article · Tue Nov 01 04:00:00 EST 1988 · Theor. Math. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01017489· OSTI ID:6167046

Maier, I O

The first confluent form of Wynn's element of algorithm is used in the Borel summation of some divergent perturbation-theory series that satisfy a strong asymptotic condition. The summation procedure reduces to the calculation of a sequence of ratios of Hankel functional determinants composed of a Borel integral and its derivatives and can be regarded as an alternative to the Pade and Pade-Borel methods. It admits a simple generalization to the summation of multiple series. The perturbation series for the ground-state energy of the anharmonic oscillator, Yukawa potential, and charmonium potential are analyzed; the critical exponents of the O(n)-symmetric Phi/sup 4/ theories (models of phase transitions) for n = 0, 1, 2, 3 and the dilute Ising model are determined.

• Research Organization: Electrotechnical Institute, Leningrad (USSR)
• OSTI ID: 6167046
• Journal Information: Theor. Math. Phys.; (United States), Journal Name: Theor. Math. Phys.; (United States) Vol. 75:2; ISSN TMPHA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
ANHARMONIC OSCILLATORS
BESSEL FUNCTIONS
BOSONS
BOUNDARY CONDITIONS
CHARMONIUM
CONVERGENCE
CRYSTAL MODELS
DYNAMICAL GROUPS
ELECTRONIC EQUIPMENT
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUIPMENT
FIELD THEORIES
FUNCTIONS
GROUND STATES
HADRONS
INTEGRAL TRANSFORMATIONS
INTEGRALS
ISING MODEL
LIE GROUPS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICS
MECHANICS
MESONS
NUCLEAR POTENTIAL
O GROUPS
OSCILLATORS
PADE APPROXIMATION
PARTICLE MODELS
PERTURBATION THEORY
PHASE TRANSFORMATIONS
PHI4-FIELD THEORY
POTENTIALS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUARKONIUM
SERIES EXPANSION
SET THEORY
SYMMETRY GROUPS
TRANSFORMATIONS
YUKAWA POTENTIAL