Perturbation theory at large order. I. The phi/sup 2//sup N/ interaction

Journal Article · Tue Mar 15 04:00:00 EST 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.1544· OSTI ID:7120183

Brezin, E; Le Guillou, J C; Zinn-Justin, J

A new method for calculating the large orders of perturbation theory in quantum field theories has been discussed recently by Lipatov. We show that the same method applied to anharmonic oscillators in quantum mechanics allows one to rederive and generalize results previously obtained by Bender and Wu. We have also verified and generalized Lipatov's results to the case of an internal O(n) symmetry. These results show the divergence of the Wilson-Fisher epsilon expansion and indicate its Borel summability which is used for critical exponents. Similarly, the Callan-Symanzik functions for the phi/sup 4/ theory in three dimensions are characterized.

• Research Organization: Service de Physique Theorique, Centre d' Etudes Nucleaires de Saclay, BP N/sup o/ 2: 91190 Gif-sur-Yvette, France
• OSTI ID: 7120183
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 15:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ENERGY LEVELS
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
GROUND STATES
HAMILTONIANS
MATHEMATICAL OPERATORS
MECHANICS
OSCILLATION MODES
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
RENORMALIZATION