Rayleigh-Schr\"odinger series and Birkhoff decomposition
  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. 
Jean-Christophe Novelli (LIGM), Thierry Paul (CMLS), David Sauzin   (IMCCE), Jean-Yves Thibon (LIGM)
math.AP math-ph math.MP