Quantum Loop Expansion to High Orders, Extended Borel Summation, and Comparison with Exact Results
Amna Noreen, Kåre Olaussen · Physical Review Letters · 2013
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 occurrence of exponential corrections but their seeming lack of any physical origin which we find surprising and puzzling.