Mathematics

A simplified model describing a Dirac electron field coupled with a classically moving point nucleus is presented and studied. The model is a semi-relativistic extension of corresponding time dependent Hartree-Fock equations coupled with classical nuclear dynamics, already known and studied both in quantum chemistry and in rigorous mathematical literature. In the course of the analysis a second result of independent interest is discussed, namely the construction of the propagator for the Dirac operator with moving point singularities, inspired to previous work of Kato and Yajima. The results have been obtained in collaboration with Federico Cacciafesta and Anne-Sophie de Suzzoni.