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arXiv · 1709.05317

A Dirac field interacting with point nuclear dynamics

Federico Cacciafesta·Anne-Sophie de Suzzoni·Diego Noja
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Abstract

The system describing a single Dirac electron field coupled with classically moving point nuclei is presented and studied. The model is a semi-relativistic extension of corresponding time-dependent one-body Hartree-Fock equation coupled with classical nuclear dynamics, already known and studied both in quantum chemistry and in rigorous mathematical literature. We prove local existence of solutions for data in $H^s$ with $s>1$ and local well posedness in $H^s$ for $s>3/2$. In the course of the analysis a second new result of independent interest is discussed and proved, namely the construction of the propagator for the Dirac operator with several moving Coulomb singularities.

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Federico Cacciafesta, Anne-Sophie de Suzzoni, Diego Noja. 2017-09-15. A Dirac field interacting with point nuclear dynamics. https://arxiv.org/abs/1709.05317

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