Perturbation theory at large order. II. Role of the vacuum instability

Journal Article · Mon Mar 14 23:00:00 EST 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.1558· OSTI ID:7225933

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

We extend our previous study of large orders of perturbation series for nonrelativistic quantum mechanics and boson field theories to more complicated situations. It is shown that when perturbation theory is performed around an unstable vacuum and does not reveal any pathology at low orders the existence of real pseudoparticles, which are responsible for the tunneling to a more stable vacuum, also implies the divergence and the non-Borel-summability of the series. Conversely, large orders of perturbations around a stable vacuum are dominated by complex solutions to Euclidean field equations. They quantitatively characterize its behavior and indicate the Borel summability of the series. Thus the corresponding Green's functions are unambiguously determined by their perturbation series.

• Research Organization: Service de Physique Theorique, Centre d'Etudes Nucleaires de Saclay, BP No 2: 91190 Gif-sur-Yvette, France
• OSTI ID: 7225933
• 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

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
COUPLING CONSTANTS
ELEMENTARY PARTICLES
EQUATIONS
FIELD EQUATIONS
FUNCTIONS
GREEN FUNCTION
HAMILTONIAN FUNCTION
MASSLESS PARTICLES
MECHANICS
PERTURBATION THEORY
QUANTUM MECHANICS
RENORMALIZATION
SCALAR FIELDS
SYMMETRY BREAKING
VACUUM STATES