Quantum Bubble Nucleation beyond WKB: Resummation of Vacuum Bubble Diagrams

TL;DR

This paper introduces a Borel resummation method to improve the calculation of quantum bubble nucleation rates, extending beyond traditional WKB approaches, and validates it through high-order perturbation series and vacuum bubble diagram calculations.

Contribution

It presents a systematic resummation technique for bubble nucleation rates in quantum field theory, surpassing the limitations of WKB approximation.

Findings

Validated in D=1 quantum mechanics using high-order perturbation series.

Extended calculations to D=2 with five-loop vacuum bubble diagrams.

Demonstrated improved accuracy in nucleation rate predictions.

Abstract

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable super-renormalizable field theory, $D$ dimensional O(N) symmetric $\phi^4$ model ($D<4$) with an attractive interaction. The validity of our proposal is tested in D=1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D=2, based on an explicit calculation of vacuum bubble diagrams to five loop orders.