Spectral and scattering theory of QFT models – SQFT

The purpose of this ANR project is the mathematical analysis of models arising from Quantum Field Theory (QFT). We plan to reach a better understanding of the dynamics associated to various QFT models by studying their spectral and scattering properties.
In the recent years, spectral and scattering theories of Pauli-Fierz-type models in Minkowski space-time have been intensively studied, in particular the Nelson model and the standard model of non-relativistic Quantum Electrodynamics (QED). The inherent difficulty in the mathematical study of these models is that, according to the physics, the mass of the field particles vanishes, which leads to the famous infrared problem as well as to several other related questions. In this project, as far as massless Pauli-Fierz models are concerned, we will aim at making progress in the resolution of important open problems, namely the proof of asymptotic completeness and the study of the resolvent of the Hamiltonian near resonances.
Our second main task will concern the mathematical analysis of QFT models associated to other physical situations. First, we will consider spectral and scattering theories for models of QFT in a curved space-time. Second, we will analyze the spectral properties of certain models of relativistic QED and of the weak interaction.
This project will enable the reinforcement and the development of collaborations between the members of our group. It is expected to lead to the resolution of very challenging problems in the mathematical analysis of Quantum Field Theory.