Calculation Rule for Aoyama-Tamra's Prescription for Path Integral with Quantum Tunneling

TL;DR

This paper derives a calculation rule for Aoyama-Tamra's path integral prescription with degenerated minima, enabling systematic computation of non-perturbative corrections and analyzing Borel summability in quantum tunneling scenarios.

Contribution

It introduces a simple, systematic calculation rule for Aoyama-Tamra's prescription, clarifying its applicability to finite and zero temperature quantum systems.

Findings

Non-perturbative corrections can be systematically computed.

The prescription yields Borel summable series at finite temperature.

The advantage diminishes at zero temperature or infinite volume.

Abstract

We derive a simple calculation rule for Aoyama--Tamra's prescription for path integral with degenerated potential minima. Non-perturbative corrections due to the restricted functional space (fundamental region) can systematically be computed with this rule. It becomes manifest that the prescription might give Borel summable series for finite temperature (or volume) system with quantum tunneling, while the advantage is lost at zero temperature (or infinite volume) limit.