Higher orders of perturbation theory and summation of series in quantum mechanics and field theory

Journal Article · Wed Feb 01 00:00:00 EST 1978 · Sov. Phys. - JETP (Engl. Transl.); (United States)

OSTI ID:6400457

Popov, V S; Eletskii, V L; Turbiner, A V

The Borel method of summation of a perturbation-theory series with factorially increasing coefficients is considered. The connection between the asymptotic form of the coefficients a/sub k/ of this series for k..-->..infinity and the nature of the singularity of the sum is established. An improved perturbation theory is constructed and the limits of its region of applicability are found. The results obtained are verified for a number of physical problems (the Lagrange function in the nonlinear electrodynamics of the vacuum, the energy levels of an electron in the Coulomb field of a nucleus with Z>137, the screening of the nuclear charge by the vacuum shell of a supercritical atom, and the Stark effect in the hydrogen atom) for which the coefficients of the perturbation-theory series increase factorially and for which, at the same time, (analytically or numerically) exact solutions are known. Application of the improved perturbation theory to the gphi/sup 4//4exclamation scalar field theory makes it possible to establish the behavior of the Gell-Mann--Low function psi (g) for 0< or approx. =0.3. In this interval psi (g) is a monotonically increasing function of the coupling constant g.

• Research Organization: Institute of Theoretical and Experimental Physics
• OSTI ID: 6400457
• Journal Information: Sov. Phys. - JETP (Engl. Transl.); (United States), Vol. 47:2
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
PERTURBATION THEORY
QUANTUM MECHANICS
COULOMB FIELD
COUPLING CONSTANTS
ENERGY LEVELS
HYDROGEN
SCALAR FIELDS
SERIES EXPANSION
SINGULARITY
STARK EFFECT
WAVE FUNCTIONS
CRYOGENIC FLUIDS
ELECTRIC FIELDS
ELEMENTS
FIELD THEORIES
FLUIDS
FUNCTIONS
MECHANICS
NONMETALS
657002* - Theoretical &amp; Mathematical Physics- Classical &amp; Quantum Mechanics
645400 - High Energy Physics- Field Theory