Quantum loop expansion to high orders, extended Borel summation, and comparison with exact results

TL;DR

This paper compares high-order quantum loop expansion predictions with exact results in a quantum mechanical model, revealing unexpected exponentially small corrections lacking clear physical explanation.

Contribution

It demonstrates that quantum loop expansions contain exponentially small corrections not attributable to instantons, challenging existing understanding of their physical origin.

Findings

Exponential corrections exist beyond all orders in the loop expansion.

These corrections cannot be explained by instanton effects.

The lack of physical origin for these corrections is surprising and puzzling.

Abstract

We compare predictions of the quantum loop expansion to (essentially) infinite orders with (essentially) exact results in a simple quantum mechanical model.We find that there are exponentially small corrections to the loop expansion, which cannot be explained by any obvious "instanton" type corrections. It is not the mathematical occurence of exponential corrections, but their seemingly lack of any physical origin, which we find surprising and puzzling.