A Dirac field interacting with point nuclear dynamics

TL;DR

This paper develops a semi-relativistic model coupling a Dirac electron with moving nuclei, proving local existence of solutions and constructing a propagator for the Dirac operator with Coulomb singularities.

Contribution

It introduces a new model combining Dirac fields with classical nuclear dynamics and proves local well-posedness and a novel propagator construction for singular Coulomb potentials.

Findings

Proved local existence of solutions for data in H^s with s>1.

Established local well-posedness in H^s for s>3/2.

Constructed the propagator for the Dirac operator with multiple moving Coulomb singularities.

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.