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For a large class of quantum mechanical models of matter and radiation wedevelop an analytic perturbation theory for non-degenerate ground states. Thistheory is applicable, for example, to models of matter with static nuclei andnon-relativistic electrons that are coupled to the UV-cutoff quantizedradiation field in the dipole approximation. If the lowest point of the energyspectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that thiseigenvalue is an analytic function of the nuclear coordinates and of$\alpha^{3/2}$, $\alpha$ being the fine structure constant. A suitably chosenground state vector depends analytically on $\alpha^{3/2}$ and it is twicecontinuously differentiable with respect to the nuclear coordinates.

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation