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 occurence of exponential corrections, but their seemingly lack of any physical origin, which we find surprising and puzzling. 
Amna Noreen, K{\aa}re Olaussen
math-ph math.MP physics.comp-ph quant-ph