Coulomb scattering in the massless Nelson model II. Regularity of ground states

Understand

For the massless Nelson model we provide detailed information about the dependence of the normalized ground states $\check{\psi}_{P,\sigma}$ of the fiber single-electron Hamiltonians $H_{P,\sigma}$ on the total momentum $P$ and the infrared cut-off $\sigma$.

• This information is obtained with the help of the iterative analytic perturbation theory.
• In particular, we derive bounds of the form \[ \|\partial_{P_i}\check{\psi}_{P,\sigma}\|,\ \| \partial_{P_i} \partial_{P_j}\check{\psi}_{P,\sigma} \|\leq \frac{c}{\sigma^{\delta_{\lambda_0}}}, \] for some constant $c$ and a function of the maximal admissible coupling constant $\lambda_0\mapsto \delta_{\lambda_0}$ s.t.
• $\lim_{\lambda_0\to 0}\delta_{\lambda_0}=0$.