Properties of the NESC and UESC Equations

There are other differences between UESC and NESC that give further reasons for preferring the latter. To examine these differences, we use perturbation theory and exploit the fact that NESC may in fact be obtained by an unnormalized Foldy-Wouthuysen transformation of the Dirac Hamiltonian and metric matrices. The transformation can be written in terms of X as 

The NESC Hamiltonian is just and the NESC metric is. These arise naturally 

We now make use of the transformed Hamiltonian to develop a perturbation theory for both NESC and UESC. The NESC partitioning is 

Y++ and Q++ are 0(c ). In both cases we have a block-diagonal zeroth-order 

Hamiltonian, and the solutions have nonzero components in either the positive- or the negative-energy space. 

---