Description
I will explain the relation of ultra-violet renormalisation to the theory of singular perturbations of self-adjoint operators in some examples from non-relativistic quantum field theory.
After introducing the relevant formalism, I will discuss in detail a toy model of particle creation and annihilation at a point source.
I will then outline how the same approach can be extended to more interesting models in which non-relativistic particles interact with a quantum field.
An example is the Bogoliubov-Fröhlich Hamiltonian, modelling the interaction of an impurity in a Bose-Einstein Condensate with the field of Bogoliubov excitations.
