Path-Integral for Quantum Tunneling

TL;DR

This paper investigates path-integral methods for theories with degenerate vacua, addressing non Borel-summability issues in perturbation theory and proposing a new Borel-summable series approach for small coupling regimes.

Contribution

It introduces a novel prescription for small coupling in path-integral formulations that results in a Borel-summable series, improving upon traditional perturbative methods.

Findings

The non Borel-summability of perturbation series is analyzed.

A new prescription yields a Borel-summable series at low orders.

The approach differs from ordinary perturbation theory by nonperturbative amounts.

Abstract

Path-integral for theories with degenerate vacua is investigated. The origin of the non Borel-summability of the perturbation theory is studied. A new prescription to deal with small coupling is proposed. It leads to a series, which at low orders and small coupling differs from the ordinary perturbative series by nonperturbative amount, but is Borel-summable.