Quantum loop expansion to high orders, extended Borel summation, and comparison with exact results.
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.
Institutt for Fysikk, Norges Teknisk-Naturvitenskapelige Universitet, N-7491 Trondheim, Norway. aamnanoreen12@gmail.com
Amna
A
Noreen
Kåre
K
Olaussen