  Coordinate noncommutativity, rather than being introduced through
deformations of operator products, is achieved by coupling an auxiliary system
with large energy excitations to the one of interest. Integrating out the
auxiliary dynamics, or equivalently taking ground state expectation values,
leads to the desired coordinate noncommutativity. The product responsible for
this noncommutativity is different from the Groenewold-Moyal one. For products
of operators at unequal times, this procedure differs from the normal,
commutative one, for time differences smaller than ones characterized by the
auxiliary system; for larger times the operator algebra reverts to the usual
one.
