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

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.Comment: 47 page

Instability of a Pseudo-Relativistic Model of Matter with Self-Generated Magnetic Field

For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all positive values of the fine structure constant. This is true no matter whether this interaction is accounted for by the Breit potential, by an external magnetic field which is chosen to minimize the energy, or by the quantized radiation field.Comment: 13 pages, AMS-LaTe