AG Mathematische Physik, Benjamin Hinrichs (Paderborn): On Infrared and Ultraviolet Problems for Polaron Models

Benjamin Hinrichs (Paderborn)

On Infrared and Ultraviolet Problems for Polaron Models
Abstract:

Polaron models describe linear interactions between quantum
matter and bosonic quantum fields, which appear in various
applications ranging from quantum optics (spin boson model) over
effective models for impurities in many-body systems (Fröhlich or
Bose polarons) to simplified versions of quantum field theories
(Nelson model). Both low-energy (infrared) and high-energy
(ultraviolet) bosons give rise to singularities.
While these singularities differ in their physical origin and
mathematical implications, they also exhibit analogous
mathematical structures. We discuss older results on the
implications of IR and UV singularities and a novel wavefunction
renormalization scheme, suitable to address both infrared and
ultraviolet problems, especially for supercritical interactions
beyond reach for simpler renormalization techniques. The latter is
based on joint work with Marco Falconi and Javier Valentín Martín.