Marco Falconi - Wave Function Renormalization for Particle-Field Interactions
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UMPA, ENS de Lyon
In this talk I will discuss the renormalization of models describing non-relativistic matter interacting with a bosonic field.
The natural approach to these models, dating back to the seminal work by E. Nelson in the sixties of last century, is to construct the renormalized Hamiltonian through the subtraction of divergent counterterms (energy and mass renormalization), implemented by a unitary transformation in the Fock space, that takes the name of dressing (or Gross) transformation. There are situations, however, in which such "additive" renormalization is
not enough: the ground state of the theory is too singular to be defined in the Fock representation, and the dressing transformation becomes ill-defined; in these cases, a wave function renormalization is necessary.
In the first part of the talk, I will introduce the wave function renormalization
procedure - that in this context is originally due to J. Glimm - and I will apply it to a toy model. In the second part of the talk I will discuss the application of these techniques to the ultraviolet renormalization of the Spin-Boson Hamiltonian, and to the infrared renormalization of the Nelson Hamiltonian.
The talk is based on joint works with B. Hinrichs and J. Valentín Martín (Paderborn).