Valley approximation for the Borel function

Journal Article · Fri Feb 14 23:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.1240· OSTI ID:7206202

Kikuchi, H ^[1]

---

1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606 (Japan)

A simple one-dimensional integral is investigated as a model for large-order estimation of the perturbative expansion in quantum mechanics with degenerate vacua. A Borel function analysis allows us to separate nonperturbative contributions from perturbative ones. Issues such as the cancellation between the perturbative and nonperturbative contributions of ambiguity due to non-Borel summability and the large-order estimation in terms of a dispersion integral are discussed. A stationary-point approximation for the Borel function is proposed to connect the simple integral to the quantum-mechanical case based on the new valley trajectory, which was recently formulated.

• OSTI ID: 7206202
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 45:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
BARYON NUMBER
CALCULATION METHODS
COUPLING CONSTANTS
INSTANTONS
INTEGRALS
MECHANICS
PERTURBATION THEORY
QUANTUM MECHANICS
QUASI PARTICLES
SCATTERING AMPLITUDES
VACUUM STATES