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

2012/09/27 by Amna Noreen, Noreen, Amna, Kåre Olaussen +1
Computer Science · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP #physics.comp-ph #quant-ph

paper · pdf · doi:10.48550/arxiv.1209.6242

5 pages, 3 figures

arxiv created 2012/09/27 · openalex publication_date 2012/09/27 · arxiv updated 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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