seminars

[Ludwik Dabrowski]

Prof. A. Pizzo (Davis)

"Bound states, scattering, and friction in some models
of nonrelativistic quantum electrodynamics"

Monday 12 Dec. 11:00-12:15,
Tuesday 13 Dec. 14:00-15:15,
room 134, SISSA


Abstract:
The fact that photons are massless particles introduces substantial
difficulties into the mathematical analysis of the interaction
between non-relativistic quantum matter and the quantized radiation
field. These difficulties are known as the infrared problem
in non-relativistic QED. In these lectures, I consider some models
of non-relativistic QED that describe respectively:
1) The hydrogen atom interacting with the quantized radiation eld;
2) The Cerenkov radiation emitted by a charged quantum particle
in a medium when the group velocity  of the particle is larger than
the speed of light in the medium;
3) The photon-electron scattering.
First, I show how the groundstate of a non-relativistic atom coupled
to the quantized radiation eld, and its groundstate energy are
constructed by an iteration scheme relying on analytic perturbation
theory. This scheme successively removes an infrared cutoff in
momentum space groundstate and the and the groundstate energy,
to arbitrary order in the structure constant  \alpha\simeq 137.
Second, I prove that, in a model where a non-relativistic particle
is coupled to a quantized relativistic scalar Bose field,
the embedded mass shell of the particle dissolves in the continuum
when the interaction is turned on, provided the coupling constant
is sufficiently small and the fiber eigenvectors corresponding
to the putative mass shell are differentiable as functions of the
total momentum of the system. Finally, I sketch the construction
of infraparticle scattering states for Compton scattering in the
standard model of non-relativistic QED. In this construction,
an infrared cutoff initially introduced to regularize the model
is removed completely. This rigorously establishes the properties
of infraparticle scattering theory predicted in the classic work
of Bloch and Nordsieck from the 1930s, Faddeev and Kulish, and others.