, Volume 10, Issue 3, pp 577-621
Date: 27 May 2009

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

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 α3/2, α being the fine structure constant. A suitably chosen ground state vector depends analytically on α3/2 and it is twice continuously differentiable with respect to the nuclear coordinates.

Communicated by Claude Alain Pillet.
Submitted: November 24, 2008. Accepted: March 4, 2009.