Two-component Dirac equation
Quantum Physics
2016-10-21 v1
Abstract
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to investigate the underlying physics in a different perspective. For particles with small mass such as the neutrino, the leading order equation has a Hermitian effective Hamiltonian, implying there is no leakage between the upper and lower spinors. In the weak relativistic regime, the leading order corresponds to a non-Hermitian correction to the Pauli equation, which takes into account the non-zero possibility of finding the lower-spinor state and offers a more precise description.
Cite
@article{arxiv.1605.06337,
title = {Two-component Dirac equation},
author = {Da-Wei Luo and P. V. Pyshkin and Ting Yu and Hai-Qing Lin and J. Q. You and Lian-Ao Wu},
journal= {arXiv preprint arXiv:1605.06337},
year = {2016}
}