8 research outputs found
Semi- and Non-relativistic Limit of the Dirac Dynamics with External Fields
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 where the kinetic energy is
related to and , respectively. Higher-order
corrections can in principle be computed to any order in the small parameter
v/c which is the ratio of typical speeds to the speed of light. Our results
imply the dynamics for electronic and positronic states decouple to any order
in v/c << 1.
To decide whether to get semi- or non-relativistic effective dynamics, one
needs to choose a scaling for the kinetic momentum operator. Then the effective
dynamics are derived using space-adiabatic perturbation theory by Panati et. al
with the novel input of a magnetic pseudodifferential calculus adapted to
either the semi- or non-relativistic scaling.Comment: 42 page