  The momentum, electronic density, spin density, and interaction dependences
of the exponents that control the $(k,\omega)$-plane singular features of the
$\sigma =\uparrow,\downarrow$ one-electron spectral functions of the 1D Hubbard
model at finite magnetic field are studied. The usual half-filling concepts of
one-electron lower Hubbard band and upper Hubbard band are defined for all
electronic density and spin density values and the whole finite repulsion range
in terms of the rotated electrons associated with the model Bethe-ansatz
solution. Such rotated electrons are the link of the non-perturbative relation
between the electrons and the pseudofermions. Our results further clarify the
microscopic processes through which the pseudofermion dynamical theory accounts
for the $\sigma $ one-electron matrix elements between the ground state and
excited energy eigenstates.
