Hamiltonian expectation values for time-dependent Foldy-Wouthuysen transformations: Implications for electrodynamics and resolution of the external-field πN ambiguity

Although the time-dependent Foldy-Wouthuysen (FW) transformation of the ''Schroedinger'' equation ipartialpsi/partialt = Hpsi yields the transformed equation ipartialpsi'/partialt = H'psi', where psi' = Upsi and H' = UHU-1-iUpartial (U-1)/partialt, the expectation values (psi1,Hpsi/sub j/) of H are not equal to (psi/sub i/',H'psi/sub j/'), but rather, to (psi/sub i/',UHU-1psi/sub j/'). But one still has (psi/sub i/',psi/sub j/') = (psi/sub i/,psi/sub j/). I discuss implications for perturbation calculations, scattering amplitudes, electrodynamics, and the external field πN ambiguity, and look at exact special cases