  An unconstrained Hamiltonian formulation of the SU(3) Yang-Mills quantum
mechanics of spatially constant fields is given using the method of minimal
embedding of SU(2) into SU(3) by Kihlberg and Marnelius. Using a canonical
transformation of the gluon fields to a new set of adapted coordinates (a
non-standard type polar decomposition), which Abelianizes the Non-Abelian Gauss
law constraints to be implemented, the corresponding unconstrained Hamiltonian
and total angular momentum are derived. This reduces the colored spin-1 gluons
to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields.
The obtained unconstrained Hamiltonian is then rewritten into a form, which
separates the rotational from the scalar degrees of freedom. It is shown that
the chromomagnetic potential has classical zero-energy valleys for two
arbitrarily large classical glueball fields, which are the unconstrained
analogs of the well-known "constant Abelian fields". On the quantum level,
practically all glueball excitation energy is expected to go into the increase
of the strengths of these two fields. Finally, as an outlook, the
straightforward generalization to low energy SU(3) Yang-Mills quantum theory in
analogy to the SU(2) case is indicated, leading to an expansion in the number
of spatial derivatives, equivalent to a strong coupling expansion, with the
SU(3) Yang-Mills quantum mechanics constituting the leading order.
