Annales Henri Poincare
For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of alpha(3/2), alpha being the fine structure constant. A suitably chosen ground state vector depends analytically on alpha(3/2) and it is twice continuously differentiable with respect to the nuclear coordinates.
Griesemer, M., & Hasler, D. G. (2009, June). Analytic perturbation theory and renormalization analysis of matter coupled to quantized radiation. In Annales Henri Poincaré (Vol. 10, No. 3, pp. 577-621). Birkhäuser-Verlag.