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

TL;DR

This paper develops an analytic perturbation theory for non-degenerate ground states in quantum models of matter coupled to quantized radiation, showing the eigenvalues and ground states depend analytically on parameters like nuclear coordinates and the fine structure constant.

Contribution

It introduces an analytic perturbation framework applicable to matter-radiation models with UV-cutoff, establishing analyticity of ground state energies and vectors with respect to key parameters.

Findings

Ground state eigenvalues are analytic functions of nuclear coordinates and /2 power of .

Ground state vectors depend analytically on /2 and are twice differentiable in nuclear coordinates.

Applicable to models with static nuclei and non-relativistic electrons 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 $\alpha^{3/2}$, $\alpha$ 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.