Rayleigh-Schr\"odinger series and Birkhoff decomposition
Analysis of PDEs
2020-03-25 v2 Mathematical Physics
math.MP
Abstract
We derive new expressions for the Rayleigh-Schr\"odinger seriesdescribing the perturbation of eigenvalues of quantumHamiltonians. The method, somehow close to the so-called dimensionalrenormalization in quantum field theory, involves the Birkhoffdecomposition of some Laurent series built up out of explicit fullynon-resonant terms present in the usual expression of theRayleigh-Schr\"odinger series. Our results provide new combinational formulae and a new way \ff{of deriving} perturbation series in Quantum Mechanics. More generally we prove that such a decomposition provides solutions of general normal form problems in Lie algebras.
Cite
@article{arxiv.1608.01110,
title = {Rayleigh-Schr\"odinger series and Birkhoff decomposition},
author = {Jean-Christophe Novelli and Thierry Paul and David Sauzin and Jean-Yves Thibon},
journal= {arXiv preprint arXiv:1608.01110},
year = {2020}
}