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 nonzero possibility of finding the lower-spinor state and offers a more precise description.

• Received 18 May 2016
• Revised 19 August 2016

DOI:https://doi.org/10.1103/PhysRevA.94.032111