Semi- and Non-relativistic Limit of the Dirac Dynamics with External Fields

Abstract

We show how to approximate Dirac dynamics for electronic initial states by semi- and non-relativistic dynamics. To leading order, these are generated by the semi- and non-relativistic Pauli hamiltonian. Higher-order corrections can in principle be computed to any order. Our results imply the dynamics for electronic and positronic states decouple to any order. To decide whether to get semi- or non-relativistic effective dynamics, one needs to choose a scaling for the kinetic momentum operator.