  The principle of minimal energy, which has been set up in the preceding
papers for systems of non-identical particles (e.g. positronium), is now
generalized to include also identical particles. Since the latter kind of
particles feels also the exchange forces (besides the usual electromagnetic
forces), one has to deal with non-zero exchange potentials which render the
theory nonlinear, according to the non-Abelian character of Relativistic
Schroedinger Theory (RST). However, the present extension of the variational
principle refers only to the linearized version of RST in order to keep the
calculations sufficiently simple. It is also demonstrated that in RST the Dirac
particles can occur in fermionic and bosonic quantum states; and the
mathematical and physical consistency of the variational principle is validated
for both types of states (concretely the fermionic hydrogen state 2p_3/2 and
the bosonic positronium state 2^1P_1).
