For the massless Nelson model, we provide detailed information about the dependence of the normalized ground states ψP,σ of the fiber single-electron Hamiltonians HP,σ on the total momentum P and the infrared cut-off σ. This information is obtained with the help of the iterative analytic perturbation theory. In particular, we derive bounds of the form ∥∂PiψP,σ∥,∥∂Pi∂PjψP,σ∥≤ c σδΛ0, for some constant c and a function of the maximal admissible coupling constant Λ0→δΛ0 such that limΛ0→0δΛ0 = 0. These results hold both in the infrared-regular and infrared-singular cases. They are exploited in part I of this series to construct the two-electron scattering states in the infrared-regular massless Nelson model (in the absence of an infrared cut-off) along the lines of the Haag-Ruelle scattering theory. They should also be relevant to the problem of scattering of two infraparticles in the infrared-singular Nelson model, whose solution is the goal of this series of papers. Although a part of a larger investigation, the present work is written in a self-contained fashion.
Dybalski, W., Pizzo, A. (2019). Coulomb scattering in the massless Nelson model II. Regularity of ground states. REVIEWS IN MATHEMATICAL PHYSICS, 31(3) [10.1142/S0129055X19500107].
Coulomb scattering in the massless Nelson model II. Regularity of ground states
Pizzo A.
2019-01-01
Abstract
For the massless Nelson model, we provide detailed information about the dependence of the normalized ground states ψP,σ of the fiber single-electron Hamiltonians HP,σ on the total momentum P and the infrared cut-off σ. This information is obtained with the help of the iterative analytic perturbation theory. In particular, we derive bounds of the form ∥∂PiψP,σ∥,∥∂Pi∂PjψP,σ∥≤ c σδΛ0, for some constant c and a function of the maximal admissible coupling constant Λ0→δΛ0 such that limΛ0→0δΛ0 = 0. These results hold both in the infrared-regular and infrared-singular cases. They are exploited in part I of this series to construct the two-electron scattering states in the infrared-regular massless Nelson model (in the absence of an infrared cut-off) along the lines of the Haag-Ruelle scattering theory. They should also be relevant to the problem of scattering of two infraparticles in the infrared-singular Nelson model, whose solution is the goal of this series of papers. Although a part of a larger investigation, the present work is written in a self-contained fashion.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.