M. Griesemer, D. Hasler
Analytic Perturbation Theory and Renormalization Analysis of Matter
Coupled to Quantized Radiation
(496K, pdf)
ABSTRACT. 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.