Renormalons in quantum mechanics

Abstract

We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac $\delta$-potential -- known to require renormalization -- and a 1d Dirac $\delta$-potential tilted at an angle. We argue that renormalons are not specific to this example and exist for a much wider class of potentials. The ambiguity in the Borel summation of the perturbative series due to the renormalon pole is resolved by the physical condition of causality through careful consideration of the $i\epsilon$ prescription. The suitably summed perturbative result coincides with the exact answer obtained through the operator formalism for scattering.

arXiv comment26 pages, 4 figures; v2 published version

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Cited by in corpus (7)

• Renormalons in integrable field theories
• Resurgence of the Renormalization Group Equation
• Resurgence and renormalons in the one-dimensional Hubbard model
• A new renormalon in two dimensions
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Perturbative study of large $N$ principal chiral model with twisted reduction